Combined and Hidden Shapes Worksheets, Questions and Revision

Question 1

0 marks

Choose an answerA) A pentagon (house outline) with vertices (0,0), (3,0), (3,3), (1.5,5), (0,3): a square with a symmetrical triangular roof centred on top, apex 2 units above the square's top edge.B) The same pentagon but with the apex moved to (2.5,5): the roof is the same height but is shifted to the right, off-centre.C) The same pentagon but with the apex at (1.5,4): the roof is centred but only 1 unit tall instead of 2, so it looks too flat.D) A square with a triangular bump attached to its right-hand edge instead of the top: vertices (0,0), (3,0), (3,3), (5,1.5), (0,3) with the triangle apex pointing right.E) The same house pentagon as A, but with an extra horizontal line drawn across the roof at y = 3 from (0,3) to (3,3), i.e. the join line has been left in instead of erased.

Question 2

1 mark

Choose an answerA) The same triangle as E (base 4, height 3, right angle bottom-right) but drawn with the hypotenuse as two short straight segments meeting in a slight bend rather than one single straight line.B) A right-angled triangle with a horizontal base of 3 units and a vertical side of 4 units, right angle at the bottom-right corner (the two leg lengths have been swapped).C) A right-angled triangle with a horizontal base of 4 units and a vertical side of 3 units, but with the right angle at the bottom-left corner instead.D) An isosceles triangle with two equal sides of 4 units and a base of 3 units, with no right angle anywhere.E) A right-angled triangle with a horizontal base of 4 units and a vertical side of 3 units on the right, the right angle at the bottom-right corner, hypotenuse sloping from top-right down to bottom-left.

Question 3

1 mark

Choose an answerA) A right trapezoid with vertices (0,0), (6,0), (4,2), (0,2): a single straight bottom edge of 6 units, a straight top edge of 4 units, a vertical left side of 2 units, and a slanted right side running from (6,0) up to (4,2).B) A trapezoid with vertices (0,0), (6,0), (6,2), (2,2): the slant is on the left-hand side instead of the right.C) A trapezoid with vertices (0,0), (6,0), (4,3), (0,3): the same bottom and top widths, but the whole shape is 3 units tall instead of 2.D) A trapezoid the same shape as A but scaled down, with vertices (0,0), (5,0), (3.5,1.5), (0,1.5).E) The same trapezoid as A, but with an extra vertical line drawn at x = 4 from (4,0) to (4,2), i.e. the original shared edge has been left visible instead of erased.

Question 4

1 mark

Choose an answerA) An isosceles right-angled triangle with a horizontal base of 4 units along the bottom of the square and its apex directly above the centre of that base, the right angle at the apex.B) The same isosceles triangle (base 4, two equal sloping sides) but with the right angle at one of the base corners instead of at the apex.C) A scalene triangle with a base of 4 units where one sloping side is noticeably longer than the other, so the apex is not above the centre of the base.D) An equilateral triangle with all three sides equal to 4 units and no right angle.E) The same isosceles right-angled triangle as A, but with the apex pointing downward, below the base line, instead of upward into the square.

Question 5

1 mark

Choose an answerA) The same step shape as E, but with the base rectangle only 4 units wide instead of 5: vertices (0,0), (4,0), (4,4), (2,4), (2,2), (0,2).B) The mirror image of E, with the small square step at the top-left instead of the top-right: vertices (0,0), (5,0), (5,2), (2,2), (2,4), (0,4).C) A shape with two steps instead of one, as though the small square were centred rather than flush against the right-hand edge: vertices (0,0), (5,0), (5,2), (3.5,2), (3.5,4), (1.5,4), (1.5,2), (0,2).D) The same step shape as E, but with the added square only 1 unit tall instead of 2, so the top of the step only reaches height 3: vertices (0,0), (5,0), (5,3), (3,3), (3,2), (0,2).E) A step-shaped hexagon with vertices (0,0), (5,0), (5,4), (3,4), (3,2), (0,2): a single straight right-hand edge running all the way from (5,0) up to (5,4), a small square step at the top-right, and the remaining left-hand part of the rectangle's top edge left at height 2.

Question 6

1 mark

Choose an answerA) The same triangle as E (legs 3 and 4, right angle top-right) but with the hypotenuse drawn as two short straight segments meeting at a slight bend rather than one single straight line.B) A right-angled triangle with legs of 4 and 4 units (an isosceles right triangle) rather than 3 and 4.C) A triangle with sides 3, 4 and 5 units, but with the right angle between the sides of length 4 and 5 instead of between 3 and 4.D) A right-angled triangle with legs of 3 and 5 units meeting at the right angle.E) A right-angled triangle with a horizontal leg of 3 units along the top edge and a vertical leg of 4 units down the right-hand edge, the right angle at the top-right corner of the rectangle, hypotenuse sloping from (3,4) down to the bottom-right corner at (6,0).

Question 7

1 mark

Choose an answerA) A pentagon with vertices (2,0), (4,2), (4,4), (2,4), (0,2): the diamond with a small square-cornered bump sticking outward on its top-right edge, apex of the bump at (4,4).B) A pentagon with vertices (2,0), (4,2), (2,4), (0,4), (0,2): the same diamond but with the bump on the top-left edge instead of the top-right edge.C) A pentagon the same shape as A but with the bump apex at (5,5) instead of (4,4), making the added triangle noticeably bigger.D) A pentagon with vertices (2,0), (4,2), (2.5,2.5), (2,4), (0,2): the bump points inward (a notch cut into the diamond) rather than outward.E) A pentagon with the same bump as A, but attached to an upright square with vertices (0,0), (4,0), (4,4), (0,4) instead of to the rotated diamond.

Question 8

1 mark

Choose an answerA) An isosceles triangle with two equal legs of 3 units meeting at an angle of 60 degrees rather than 90 degrees.B) An isosceles right-angled triangle with two equal legs of 4 units each rather than 3 units.C) A right-angled triangle with legs of 3 and 6 units (not isosceles).D) An isosceles right-angled triangle with two equal legs of 3 units each, one running along part of the square's right-hand edge and one running along part of the horizontal line, meeting at a right angle, with a sloping hypotenuse joining them.E) The same isosceles right-angled triangle as D (legs 3 and 3) but with its hypotenuse drawn as a slightly curved (bowed) line instead of a straight one.

Question 9

1 mark

Choose an answerA) A pentagon with the same roof, but built on an upright rectangle with vertices (0,0), (4,0), (4,3), (0,3) instead of the slanted parallelogram.B) The same pentagon but with the apex at (4,5) instead of (3,5), so the roof is shifted to the right.C) The same pentagon but with the apex at (3,4) instead of (3,5), so the roof is only 1 unit tall instead of 2.D) A pentagon with vertices (0,0), (4,0), (5,3), (3,5), (1,3): the parallelogram with a symmetrical roof centred on its slanted top edge, apex 2 units above the midpoint of that edge.E) The same pentagon shape as D, but with the apex at (3,1), so the roof points downward into the parallelogram instead of upward and outward.

Question 10

1 mark

Choose an answerA) A right-angled triangle with two equal legs of 5 units each.B) A right-angled triangle with legs of 8 and 3 units meeting at the top-right corner.C) A right-angled triangle with a horizontal leg of 8 units along the top edge and a vertical leg of 5 units down the right-hand edge, right angle at the top-right corner.D) A right-angled triangle with legs of 8 and 5 units, but with the right angle at the bottom-right corner instead of the top-right corner.E) The same triangle as C (legs 8 and 5, right angle top-right) but with its longest side drawn as two straight segments meeting at a slight kink rather than one single line.

Question 11

1 mark

Choose an answerA) The same pentagon outline as B, but the whole shape - both the square part and the triangular part - is filled with the grey hatching.B) A pentagon with vertices (0,4), (4,4), (4,0), (2,-3), (0,0): the top 4-by-4 square region (from y = 0 to y = 4) is filled with 45 degree grey hatching, and the triangular point below (apex at (2,-3)) is left completely white, with a solid black outline throughout and no internal line at the join.C) The same pentagon outline as B, but the shading is reversed: the triangular part is hatched grey and the square part is left white.D) The same pentagon outline and shading distribution as B, but the hatching lines are drawn vertical instead of at 45 degrees.E) The same pentagon outline and shading distribution as B, but with the join between the square part and the triangular part shown as a dashed line rather than no line at all.

Question 12

1 mark

Choose an answerA) The same right-angled triangle (legs 6 and 4, right angle bottom-right) but left completely white, unshaded.B) A right-angled triangle with legs 6 (horizontal) and 4 (vertical), right angle at the bottom-right corner, filled solid grey.C) The same right-angled triangle (legs 6 and 4, right angle bottom-right) filled with a striped hatch pattern instead of a solid grey fill.D) A right-angled triangle with two equal legs of 4 units each, filled solid grey.E) A right-angled triangle with legs 6 and 4, right angle at the top-left corner instead of the bottom-right, filled solid grey.

Question 13

1 mark

Choose an answerA) The same pentagon but with the apex at (3,4) instead of (3,5.5), making the roof noticeably shorter.B) The same pentagon but with the apex at (3.5,5.5) instead of (3,5.5), so the roof is shifted right.C) A pentagon with vertices (0,0), (6,0), (4,3), (3,5.5), (2,3): the trapezoid with a symmetrical roof centred on its top edge, apex 2.5 units above the midpoint of that edge.D) A hexagon formed by attaching the triangle to the trapezoid's left slanted edge, from (0,0) to (2,3), instead of to the top edge.E) The same pentagon shape as C, but with the apex at (3,1.5), so the roof points down into the trapezoid instead of up and out.

Question 14

1 mark

Choose an answerA) An isosceles triangle whose two equal sides (not the base) are 4 units long rather than 3 units.B) A right-angled isosceles triangle with two equal legs of 3 units, but with the right angle located at the midpoint of a side instead of at an outer corner.C) A right-angled triangle with legs of 3 and 4 units (not isosceles).D) A right-angled isosceles triangle with two equal legs of 3 units, its right angle located exactly at one of the outer square's corners, hypotenuse joining two adjacent edge-midpoints.E) The same right-angled isosceles triangle as D (legs 3 and 3, right angle at the corner) but with its hypotenuse drawn as a dashed line instead of a solid one.

Question 15

1 mark

Choose an answerA) A square, 4 units by 4 units, instead of a 4 by 3 rectangle.B) The same 4 by 3 rectangle as C, but with the diagonal from (4,0) to (0,3) still drawn as a visible internal line.C) A plain rectangle, 4 units wide and 3 units tall, with vertices (0,0), (4,0), (4,3), (0,3), and no internal line.D) A slanted parallelogram, 4 units wide and 3 units tall, with no right angles at its corners.E) A rectangle with the same area but oriented the other way round: 3 units wide and 4 units tall.

Question 16

1 mark

Choose an answerA) The same isosceles triangle as E, but with its vertical base on the right-hand edge drawn as a dashed line instead of solid.B) The mirror image of E: apex pointing right, with the short vertical base of 2 units on the left-hand edge instead of the right.C) The same isosceles triangle as E (apex left, base on the right edge) but with the vertical base being 4 units long instead of 2.D) A scalene (non-isosceles) triangle in the same rough position as E, with its apex noticeably above or below the mid-height line rather than exactly level with it.E) An isosceles triangle with its apex pointing left, a short vertical base of 2 units on the right-hand edge of the square, positioned symmetrically about half the square's height (y = 3).

Question 17

1 mark

Choose an answerA) The same overall shape as D, but with the slanted top edge running from (4,4) to (1,8) instead of (0,8).B) A quadrilateral with vertices (0,0), (4,0), (4,8), (0,4): the slant is on the right-hand side instead of the left.C) A pentagon with vertices (0,0), (4,0), (4,4), (0,8), (0,4): the same overall outline as D, but with an unnecessary kink shown at (0,4) instead of one continuous straight edge on the left.D) A quadrilateral with vertices (0,0), (4,0), (4,4), (0,8): one long straight left-hand edge running all the way from (0,8) down to (0,0) (8 units), a bottom edge of 4 units, a right-hand edge of 4 units, and a slanted top edge from (4,4) up to (0,8).E) A square with vertices (0,0), (4,0), (4,4), (0,4) shown with a separate, unattached triangle floating above it, rather than a single joined outline.

Question 18

1 mark

Choose an answerA) An isosceles triangle with a base of 8 units and two equal sloping sides of 6 units each.B) An isosceles triangle with a base of 8 units along the top or bottom edge and two equal sloping sides of 5 units each, apex at the centre of the rectangle.C) An isosceles triangle with a base of 5 units and two equal sloping sides of 8 units each.D) A right-angled (non-isosceles) triangle with a base of 8 units and a height of 3 units, right angle at one end of the base.E) The same isosceles triangle as B (base 8, equal sides 5) but with the two equal sides drawn slightly bowed rather than straight.

Question 19

1 mark

Choose an answerA) An isosceles triangle with a base of 10 units but a height of 5 units instead of 3.B) A triangle with a base of 10 units, but with the apex positioned above a point 3 units from the left end of the base rather than above the centre (a scalene triangle).C) An isosceles triangle with a base of 10 units running from (-5,0) to (5,0) and an apex at (0,3), directly above the centre of the base.D) An isosceles triangle with a base of 6 units instead of 10, apex height 3.E) The same isosceles triangle as C (base 10, height 3, apex centred) but with a visible vertical line drawn from the apex down to the midpoint of the base.

Question 20

1 mark

Choose an answerA) The same isosceles triangle as E (base 4, height 3) but drawn visibly squashed, as though its height were only 2 instead of 3.B) An isosceles triangle with a base of 4 units and its apex 4 units from the base rather than 3.C) An isosceles triangle with a base of 6 units and its apex 3 units from the base.D) A scalene triangle with a base of 4 units whose apex is offset to one side rather than centred above the midpoint.E) An isosceles triangle with a base of 4 units (matching the hexagon's bottom or top edge) and its apex 3 units directly above or below the centre of that base.

Question 21

1 mark

Choose an answerA) The same triangle with the square attached on the inward side instead, so the square overlaps the triangle's own space, with vertices (0,0), (6,0), (0,8), (-8,2), (-2,-6).B) A pentagon with vertices (0,0), (6,0), (14,6), (8,14), (0,8): the right-angled triangle (legs 6 and 8) with a tilted square of side 10 attached outward on its hypotenuse.C) The same pentagon outline as B, but the attached shape is a 10 by 8 rectangle instead of a 10 by 10 square.D) The same pentagon, but with the triangle's legs swapped so the right angle triangle has a base of 8 and a height of 6 instead of a base of 6 and a height of 8, shifting the whole square's position.E) The same pentagon outline as B, but with the shared hypotenuse from (6,0) to (0,8) still shown as a faint internal line.

Question 22

1 mark

Choose an answerA) A right-angled triangle with legs of 2 and 4 units (not isosceles).B) A right-angled isosceles triangle with two equal legs of 3 units instead of 2.C) A right-angled isosceles triangle with two equal legs of 2 units, its right angle located exactly at one of the outer square's corners.D) A right-angled isosceles triangle with legs of 2 and 2, but with the right angle located at the midpoint of one of the outer square's edges rather than at a corner.E) The same right-angled isosceles triangle as C (legs 2 and 2, right angle at the corner) but with its hypotenuse drawn bulging outward rather than as a straight line.

Question 23

1 mark

Choose an answerA) The same overall shape as D, but with the step positioned at (0,2) instead of (0,4).B) The same quadrilateral as D, but with a visible kink drawn in the bottom edge at (0,0) instead of one continuous straight line from (-3,0) to (8,0).C) A triangle with vertices (-3,0), (8,0), (0,6): the small triangle's leg is shown covering the whole left-hand edge up to (0,6), with no step at (0,4) at all.D) A quadrilateral with vertices (-3,0), (8,0), (0,6), (0,4): a single straight bottom edge from (-3,0) to (8,0), a slanted edge from (8,0) up to (0,6), a short vertical step down from (0,6) to (0,4), then a slanted edge from (0,4) back to (-3,0).E) The mirror image of D, with the small triangle's step attached on the right-hand side of shape 1 instead of the left.

Question 24

1 mark

Choose an answerA) The same parallelogram but with the top and bottom sides sloping gently downward from left to right instead of upward.B) A parallelogram with two vertical sides of 5 units each and two long top-and-bottom sides that slope gently upward from left to right, each about 10 units long.C) A true rectangle (no slope at all) with vertical sides of 5 units and horizontal sides of 10 units.D) A parallelogram with vertical sides of 3 units instead of 5, sloping the same gentle way as B.E) The same parallelogram as B (vertical sides 5 units, gentle upward slope) but with the top and bottom edges drawn bowed rather than straight.

Question 25

1 mark

Choose an answerA) A pentagon with vertices (0,0), (6,0), (11,3), (7,4), (1,5): the quadrilateral with a triangular point sticking outward to the right between (6,0) and (7,4), the point of the bump at (11,3).B) A pentagon with the bump pointing inward instead, with a vertex at approximately (5,2) creating a notch rather than an outward bump.C) The same overall pentagon shape as A, but with the bump's outer point at (10,1) instead of (11,3), making the bump lower and less pronounced.D) The original quadrilateral only, enlarged, with vertices (0,0), (7,0), (8,5), (1,6), showing no added triangular bump at all.E) The same pentagon outline and vertices as A, but with the shared edge from (6,0) to (7,4) still shown as a faint internal line inside the pentagon.

Combined and Hidden Shapes - Worksheets, Questions and Revision

EP.N13 Combined and Hidden Shapes

Revision notes: Combined and Hidden Shapes

Question 1

Question 2

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Question 25

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Question 22

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Question 25