Jamal has cut a piece of card that is made from two rectangles, A and B, joined together. Rectangle A measures 7 cm by 4 cm. Rectangle B measures 3 cm by 2 cm. Work out the total area of the card.
Diagram NOT accurately drawn
(Total for Question 3 is 3 marks)
4
The diagram shows a shape made from a rectangle with a triangle on top. The rectangle is 6 cm wide and 4 cm tall. The total height of the whole shape is 7 cm.
Diagram NOT accurately drawn
(Total for Question 4 is 4 marks)
5
The diagram shows an L-shaped piece of sheet metal. Show that the area of the shape is 83 cm2.
Diagram NOT accurately drawn
(Total for Question 5 is 4 marks)
6
The diagram shows a cross-shaped garden bed made from two overlapping rectangles. The vertical rectangle measures 4 m by 12 m. The horizontal rectangle measures 10 m by 4 m. The square where they overlap measures 4 m by 4 m. Work out the total area of the garden bed.
Diagram NOT accurately drawn
(Total for Question 6 is 4 marks)
7
Priya's living room is L-shaped. It is made from a rectangle 5 m by 4 m with an alcove that adds a rectangle 2 m by 1.5 m.
Diagram NOT accurately drawn
(a)Work out the total floor area of the living room.(2)
(b)Carpet for the room costs 18.50 pounds per m2. Work out the total cost of the carpet.(2)
(Total for Question 7 is 4 marks)
8
A rectangular garden measures 15 m by 9 m. A square patio measuring 6 m by 6 m is built in one corner of the garden. The rest of the garden is grass. Work out the area of grass.
Diagram NOT accurately drawn
(Total for Question 8 is 3 marks)
9
The diagram shows a T-shaped tile. The top bar of the T is 14 cm wide and 3 cm tall. The vertical stem is 4 cm wide. The total height of the tile is 10 cm. Work out the area of the tile.
Diagram NOT accurately drawn
(Total for Question 9 is 4 marks)
10
The diagram shows an L-shaped courtyard. The bottom edge is 10 m, the left-hand edge is 7 m, the top edge is 6 m and the lower right-hand edge is 4 m. All corners are right angles.
Diagram NOT accurately drawn
(a)Work out the area of the courtyard.(3)
(b)Work out the perimeter of the courtyard.(3)
(Total for Question 10 is 6 marks)
11
The diagram shows a garage roof end made from a rectangle with a triangle on top, forming a pentagon shape. The rectangle is 8 m wide and 5 m tall. The triangle on top has a base of 8 m and a perpendicular height of 3 m. Work out the total area of the garage end.
Diagram NOT accurately drawn
(Total for Question 11 is 4 marks)
12
A rectangular picture frame measures 15 cm by 8 cm on the outside. A rectangular window measuring 6 cm by 3 cm is cut from the middle of the frame to hold the photo. Work out the area of the frame itself (not including the window).
Diagram NOT accurately drawn
(Total for Question 12 is 4 marks)
13
Kwame's garden is a rectangle 10 m by 6 m. A rectangular flowerbed 3 m by 2 m is dug in one corner. The rest of the garden is turfed.
Diagram NOT accurately drawn
(a)Work out the area to be turfed.(2)
(b)Turf costs 7.25 pounds per m2. Work out the total cost of the turf.(2)
(Total for Question 13 is 4 marks)
14
The diagram shows a bracket-shaped piece of steel. The overall shape is a rectangle 14 cm by 6 cm, with a rectangular notch cut from the middle of the top edge. The notch is 6 cm wide and 3 cm deep. Work out the area of the steel bracket.
Diagram NOT accurately drawn
(Total for Question 14 is 5 marks)
15
The diagram shows a shape made from a rectangle 6.5 cm wide and 4 cm tall, with a triangle on top sharing the same 6.5 cm base. The perpendicular height of the triangle is 2.4 cm. Work out the total area of the shape.
Diagram NOT accurately drawn
(Total for Question 15 is 4 marks)
16
A compound shape is made from a rectangle measuring 8 cm by 5 cm joined to a second rectangle that is x cm wide and 3 cm tall. The total area of the whole shape is 58 cm2. Find the value of x.
Diagram NOT accurately drawn
(Total for Question 16 is 4 marks)
17
The diagram shows a shop sign made from a rectangle with a semicircle on one end. The rectangle measures 14 cm by 8 cm. The semicircle has a diameter of 8 cm, the same as the width of the rectangle. Calculate the total area of the sign. Give your answer correct to 3 significant figures.
Diagram NOT accurately drawn
(Total for Question 17 is 4 marks)
18
Fatima and Rhys are comparing two designs for a new decked area in their garden. Design A is an L-shape: an overall rectangle 6 m by 5 m with a 2 m by 2 m corner cut off. Decking for Design A costs 24.99 pounds per m2. Design B is a rectangle 5.5 m by 4.5 m. Decking for Design B costs 26.50 pounds per m2.
Diagram NOT accurately drawn
(a)Work out the total cost of decking for Design A.(2)
(b)Work out the total cost of decking for Design B.(2)
(c)Which design should Fatima and Rhys choose if they want the cheaper decking? Give a reason, supported by your figures from parts (a) and (b).(2)
(Total for Question 18 is 6 marks)
Mark scheme · 3.18 Area of Compound Shapes
Question 1
M1 8 x 5
A1 40 (cm2) cao
Answer: 40 cm2
Question 2
M1 0.5 x 6 x 4
A1 12 (cm2) cao
Answer: 12 cm2
Question 3
M1 area of A = 7 x 4 (= 28)
M1 area of B = 3 x 2 (= 6)
A1 34 (cm2) cao
Answer: 34 cm2
Question 4
M1 height of triangle = 7 - 4 (= 3)
M1 area of rectangle = 6 x 4 (= 24)
M1 area of triangle = 0.5 x 6 x 3 (= 9)
A1 33 (cm2) cao
Answer: 33 cm2
Question 5
M1 finds one missing length, e.g. 12 - 7 (= 5) or 9 - 4 (= 5)
M1 splits shape into two rectangles, e.g. 12 x 4 and 7 x 5 (or equivalent split)
M1 adds the two areas correctly, e.g. 48 + 35 (or 108 - 25)
A1 83 (cm2) cso, with all working shown
Answer: 83 cm2 (shown)
Question 6
M1 area of vertical rectangle = 4 x 12 (= 48)
M1 area of horizontal rectangle = 10 x 4 (= 40)
M1 subtracts the overlap once, e.g. 48 + 40 - 16
A1 72 (m2) cao
Answer: 72 m2
Question 7
(a) M1 5 x 4 + 2 x 1.5
(a) A1 23 (m2) cao
(a) Answer: 23 m2
(b) M1 their (a) x 18.50, ft
(b) A1 425.50 (pounds) cao, ft from (a)
(b) Answer: GBP 425.50
Question 8
M1 15 x 9 (= 135)
M1 6 x 6 (= 36)
A1 99 (m2) cao
Answer: 99 m2
Question 9
M1 stem height = 10 - 3 (= 7)
M1 area of top bar = 14 x 3 (= 42)
M1 area of stem = 4 x 7 (= 28)
A1 70 (cm2) cao
Answer: 70 cm2
Question 10
(a) M1 finds a missing length, e.g. 10 - 6 (= 4) or 7 - 4 (= 3)
(a) M1 correct method for area, e.g. 10 x 7 - 4 x 3
(a) A1 58 (m2) cao
(a) Answer: 58 m2
(b) M1 finds both missing lengths (4 and 3)
(b) M1 adds all six side lengths
(b) A1 34 (m) cao
(b) Answer: 34 m
Question 11
M1 area of rectangle = 8 x 5 (= 40)
M1 area of triangle = 0.5 x 8 x 3 (= 12)
M1 adds the two areas
A1 52 (m2) cao
Answer: 52 m2
Question 12
M1 outer area = 15 x 8 (= 120)
M1 window area = 6 x 3 (= 18)
M1 subtracts window from outer area
A1 102 (cm2) cao
Answer: 102 cm2
Question 13
(a) M1 10 x 6 - 3 x 2
(a) A1 54 (m2) cao
(a) Answer: 54 m2
(b) M1 their (a) x 7.25, ft
(b) A1 391.50 (pounds) cao, ft from (a)
(b) Answer: GBP 391.50
Question 14
M1 overall area = 14 x 6 (= 84)
M1 notch area = 6 x 3 (= 18)
M1 identifies that the notch must be subtracted once
M1 84 - 18
A1 66 (cm2) cao
Answer: 66 cm2
Question 15
M1 area of rectangle = 6.5 x 4 (= 26)
M1 area of triangle = 0.5 x 6.5 x 2.4 (= 7.8)
M1 adds the two areas
A1 33.8 (cm2) cao
Answer: 33.8 cm2
Question 16
M1 area of rectangle 1 = 8 x 5 (= 40)
M1 forms the equation 40 + 3x = 58 (oe)
M1 3x = 18
A1 x = 6 cao
Answer: x = 6
Question 17
M1 identifies radius = 4
M1 area of rectangle = 14 x 8 (= 112)
M1 area of semicircle = 0.5 x π x 42 (awrt 25.1)
A1 awrt 137 (cm2), 3 sf
Answer: 137 cm2 (3 sf)
Question 18
(a) M1 area of A = 6 x 5 - 2 x 2 (= 26)
(a) A1 cost = 649.74 (pounds) cao
(a) Answer: GBP 649.74
(b) M1 area of B = 5.5 x 4.5 (= 24.75)
(b) A1 cost = 655.88 (pounds), awrt, cao
(b) Answer: GBP 655.88 (awrt)
(c) B1 states Design A (ft from their (a) and (b) if consistent)
(c) C1 correct reason with correct figures compared, e.g. 649.74 < 655.88 so Design A is 6.14 pounds cheaper
(c) Answer: Design A, because it is GBP 6.14 cheaper