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3.18F Area of Compound Shapes: Foundation Tier Practice

EDEXCEL Edexcel 1MA1 · Calculator allowed · about 60 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Work out the area of a rectangle that is 7 m long and 3 m wide.

(Total for Question 1 is 1 mark)

A triangle has base 8 cm and height 5 cm. Work out its area.

(Total for Question 2 is 2 marks)

The shape is made of a rectangle 6 cm by 4 cm with a right-angled triangle on top. The triangle has base 6 cm and height 3 cm. Work out the total area of the shape.

(Total for Question 3 is 3 marks)

A rectangular paving slab has area 48 m² and length 6 m. Work out the width of the slab.

(Total for Question 4 is 2 marks)

Find the area of the L-shaped figure made from two rectangles. Rectangle A is 5 m by 2 m and rectangle B is 3 m by 2 m, joined as shown so their widths line up (they share a 2 m side). Work out the total area.

(Total for Question 5 is 3 marks)

Work out the area of a trapezium with parallel sides 7 cm and 3 cm and height 4 cm. (Use area = (1/2) * (sum of parallel sides) * height.)

(Total for Question 6 is 3 marks)

A roof tile is shaped like a rectangle 12 cm by 8 cm with a small isosceles triangle attached along the short side. The triangle has base 8 cm and height 3 cm. Work out the area of one tile.

(Total for Question 7 is 4 marks)

A classroom notice board is a compound shape: a rectangle 2.0 m by 1.2 m with a small rectangle of 0.4 m by 0.6 m removed from one corner. Work out the area of the notice board to 2 decimal places in square metres.

(Total for Question 8 is 5 marks)

Work out the area of a parallelogram with base 9 cm and perpendicular height 4 cm.

(Total for Question 9 is 2 marks)

Two congruent right-angled triangles each have legs 6 cm and 8 cm. They are joined along the 8 cm sides to form a kite. Work out the area of the kite.

(Total for Question 10 is 3 marks)

A garden is made from a large rectangle 8.0 m by 5.0 m. A small rectangular pond 3.0 m by 2.0 m is removed from one corner. A triangular flowerbed with base 4.0 m and height 1.5 m is added along one long edge of the large rectangle. Work out the total area of the garden.

(Total for Question 11 is 6 marks)

A notice panel is a rectangle measuring 120 cm by 80 cm. A triangular corner is cut away; the triangle has base 30 cm and height 40 cm. Work out the area of the remaining panel in square metres. Give your answer to 2 decimal places.

(Total for Question 12 is 6 marks)

Mark scheme · 3.18F Area of Compound Shapes: Foundation Tier Practice

Question 1

B1 21 m² cao
Answer: 21 m²

Question 2

M1 uses 1/2 * base * height or equivalent method
A1 20 cm² cao
Answer: 20 cm²

Question 3

M1 area rectangle = 6 * 4 = 24 cm² or equivalent
M1 area triangle = 1/2 * 6 * 3 = 9 cm² or equivalent
A1 33 cm² cao (24 + 9)
Answer: 33 cm²

Question 4

M1 uses width = area / length or equivalent
A1 8 m cao
Answer: 8 m

Question 5

M1 area rectangle A = 5 * 2 = 10 m²
M1 area rectangle B = 3 * 2 = 6 m²
A1 16 m² cao (10 + 6)
Answer: 16 m²

Question 6

M1 substitute into formula: 1/2*(7+3)*4 or equivalent
M1 compute 1/2*10*4 = 20
A1 20 cm² cao
Answer: 20 cm²

Question 7

M1 area rectangle = 12 * 8 = 96 cm²
M1 area triangle = 1/2 * 8 * 3 = 12 cm²
A1 compute total 96 + 12 = 108 cm²
A1 108 cm² cao
Answer: 108 cm²

Question 8

M1 area large rectangle = 2.0 * 1.2 = 2.4 m²
M1 area small removed rectangle = 0.4 * 0.6 = 0.24 m²
M1 subtract removed area: 2.4 - 0.24 = 2.16
A1 give 2.16 m² to 2 decimal places
A1 2.16 m² cao
Answer: 2.16 m²

Question 9

M1 uses area = base * height: 9 * 4
A1 36 cm² cao
Answer: 36 cm²

Question 10

M1 area of one right triangle = 1/2 * 6 * 8 = 24 cm²
M1 two triangles area = 24 * 2 = 48 cm²
A1 48 cm² cao
Answer: 48 cm²

Question 11

M1 area large rectangle = 8.0 * 5.0 = 40.0 m²
M1 area pond = 3.0 * 2.0 = 6.0 m²
M1 area triangle = 1/2 * 4.0 * 1.5 = 3.0 m²
A1 subtract pond: 40.0 - 6.0 = 34.0 m²
A1 add triangle: 34.0 + 3.0 = 37.0 m²
A1 37.0 m² cao
Answer: 37.0 m²

Question 12

M1 area rectangle = 120 * 80 = 9600 cm²
M1 area triangle = 1/2 * 30 * 40 = 600 cm²
M1 subtract triangle: 9600 - 600 = 9000 cm²
M1 convert to m²: 9000 cm² = 9000 / 10000 = 0.9 m²
A1 give value to 2 dp: 0.90 m²
A1 0.90 m² cao
Answer: 0.90 m²

Area of Compound Shapes: Foundation Tier Practice - Worksheets, Questions and Revision