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KS3 · Geometry and Measures

KS3.M-G8 Area of Parallelograms, Trapezia and Compound Shapes

AQA KS3.M-G8 · Calculators not allowed · about 50 minutes

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

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

(1)

Calculate the area of a parallelogram with base 12 cm and height 3.5 cm. Give your answer in cm².

(2)

A parallelogram has base 7 m and area 42 m². Work out the height.

(2)

Find the area of a trapezium with parallel sides 6 cm and 10 cm and height 4 cm.

(2)

A trapezium has parallel sides 7.5 m and 12.5 m with height 2 m. Calculate its area in m².

(2)

A compound shape is made of a rectangle 8 cm by 5 cm and a triangle with base 8 cm and height 3 cm attached along one 8 cm side. Find the total area.

(2)

A parallelogram has base 9 cm and area 63 cm². State the height.

(1)

An L-shaped figure is made from two rectangles. One rectangle is 6 m by 3 m and the other is 4 m by 2 m. Find the total area.

(2)

A shape is made from a rectangle 10 cm by 4 cm and a trapezium attached to one 4 cm side. The trapezium has parallel sides 4 cm and 8 cm and height 3 cm. Find the total area of the shape.

(3)

A rectangle has area 45 m² and width 5 m. A parallelogram has the same area and height 9 m. Work out the base of the parallelogram.

(2)

A small parallelogram has area 2500 cm². Express this area in m².

(2)

A compound shape consists of a parallelogram with base 14 cm and height 3 cm, and a triangle on top with base 14 cm and height 4 cm. Find the total area.

(3)

A trapezium has parallel sides 9 m and 15 m and area 96 m². Work out its height.

(2)

Priya lays a parallelogram-shaped flower bed with base 6 m and height 2 m. Soil costs 3 pounds per m². Calculate the cost to cover the bed with soil.

(3)

A parallelogram has base 8 cm and height 5 cm. If the base is doubled and the height stays the same, what happens to the area? Give a number and a short reason.

(2)

A rectangle 12 m by 6 m has a right triangle removed from one corner. The triangle has legs 3 m and 4 m (right angle between them). Find the area of the remaining shape.

(3)

Explain why the area of a trapezium equals the average of the two parallel sides multiplied by the height. You may give a short diagram description or words.

(3)

Stretch: A compound shape is made from a parallelogram with base 9 cm and height 4 cm, and two congruent right triangles each with base 3 cm and height 2 cm attached to the other two sides of the parallelogram. Find the total area.

(3)

Mark scheme · KS3.M-G8 Area of Parallelograms, Trapezia and Compound Shapes

Question 1

B1 Area 8 x 5 = 40 cm² cao
Answer: 40 cm²

Question 2

M1 Use area = base x height: 12 x 3.5 or equivalent
A1 42 cm² cao
Answer: 42 cm²

Question 3

M1 Use height = area / base: 42 / 7 or equivalent
A1 6 m cao
Answer: 6 m

Question 4

M1 Use area = (a + b)/2 x height with a=6, b=10: (6+10)/2 x 4
A1 32 cm² cao
Answer: 32 cm²

Question 5

M1 Use (7.5 + 12.5)/2 x 2 or equivalent
A1 20 m² cao
Answer: 20 m²

Question 6

M1 Area rectangle 8 x 5 = 40 and triangle 1/2 x 8 x 3 = 12 used
A1 52 cm² cao
Answer: 52 cm²

Question 7

B1 height = 63 / 9 = 7 cm cao
Answer: 7 cm

Question 8

M1 Areas 6 x 3 = 18 and 4 x 2 = 8 calculated and added
A1 26 m² cao
Answer: 26 m²

Question 9

M1 Area rectangle 10 x 4 = 40 and area trapezium (4+8)/2 x 3 = 18 calculated
M1 Both areas added 40 + 18
A1 58 cm² cao
Answer: 58 cm²

Question 10

M1 Area of rectangle = 45 used as area of parallelogram; base = area / height = 45 / 9
A1 5 m cao
Answer: 5 m

Question 11

M1 Recognise 100 cm = 1 m so 1 m² = 10000 cm² or divide by 10000
A1 0.25 m² cao
Answer: 0.25 m²

Question 12

M1 Area parallelogram 14 x 3 = 42 and triangle 1/2 x 14 x 4 = 28 calculated
M1 Areas added 42 + 28
A1 70 cm² cao
Answer: 70 cm²

Question 13

M1 Use area = (a+b)/2 x h so h = area x 2 / (a+b): h = 96 x 2 / (9+15)
A1 8 m cao
Answer: 8 m

Question 14

M1 Area = 6 x 2 = 12 m² used
M1 Multiply area by cost per m²: 12 x 3
A1 36 pounds cao
Answer: 36 pounds

Question 15

M1 State new area calculation or relation: original 8 x 5 = 40 so new base 16 gives 16 x 5 = 80
A1 Area doubles to 80 cm², because area = base x height so doubling base doubles area
Answer: 80 cm²

Question 16

M1 Area rectangle 12 x 6 = 72 and triangle area 1/2 x 3 x 4 = 6 calculated
M1 Subtract triangle from rectangle: 72 - 6
A1 66 m² cao
Answer: 66 m²

Question 17

M1 Mention splitting trapezium into two triangles or rearranging into a rectangle idea, or pairing two identical trapezia to make a rectangle
M1 State that pairing two trapezia gives a rectangle with width a + b and same height so area of two trapezia = (a + b) x h
A1 Conclude area of one trapezium = (a + b)/2 x h cao
Answer: (a + b)/2 x h

Question 18

M1 Area parallelogram 9 x 4 = 36 and area of one triangle 1/2 x 3 x 2 = 3 calculated
M1 Two triangles total 3 + 3 = 6 and add to parallelogram
A1 42 cm² cao
Answer: 42 cm²

Area of Parallelograms, Trapezia and Compound Shapes - Worksheets, Questions and Revision