A rectangle has length 7 cm and width 5 cm. Write down its perimeter.
(1)
2
A square has side length 6 cm. Calculate its perimeter.
(1)
3
A triangle has sides 5 cm, 7 cm and 8 cm. Work out its perimeter.
(1)
4
Calculate the area of a rectangle with length 6 cm and width 4 cm.
(1)
5
A triangle has base 8 cm and height 5 cm. Calculate its area.
(1)
6
Two rectangles are joined along a side. Rectangle A is 6 cm by 4 cm. Rectangle B is 3 cm by 4 cm. Calculate the total area of the combined shape.
(2)
7
A rectangle has width 6 cm. Its perimeter is 30 cm. Work out the length of the rectangle.
(2)
8
The perimeter of a triangle is 27 cm. Two sides are 8 cm and 9 cm. Find the length of the third side.
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9
A rectangle measures 5 cm by 7 cm. Its length is increased by 2 cm while the width stays the same. Calculate the increase in area.
(2)
10
A triangle has base 5 cm and area 30 cm2. Work out the height of the triangle.
(2)
11
A shape is made from a rectangle and a triangle. The rectangle is 8 cm by 3 cm. The triangle has base 4 cm and height 3 cm and sits on one short side of the rectangle. Calculate the total area of the shape.
(2)
12
A right-angled triangle has legs of length 6 cm and 8 cm. Calculate its area.
(1)
13
Two rectangles are joined along a short side to make an L-shape. Rectangle A is 6 cm by 4 cm. Rectangle B is 4 cm by 3 cm and is attached so their widths of 4 cm line up at the bottom. Find the perimeter of the L-shape.
(2)
14
A rectangle has length 12 cm and area 84 cm2. Work out its width.
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15
A triangle has height 4 cm and area 18 cm2. Find the length of the base.
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16
A rectangular garden is 12 m by 8 m. A triangular flower bed with base 6 m and height 4 m is removed from one corner. Calculate the area of the garden that remains.
(2)
17
A composite shape has a rectangle of area 42 cm2 (length 7 cm) and a triangle with height 5 cm attached so that the total area of the composite shape is 100 cm2. Find the base of the triangle. Give your answer to one decimal place if necessary.
(3)
18
A triangle has base 5 cm and height 12 cm so area is 30 cm2. A rectangle has length 8 cm and unknown width w. The rectangle and triangle have the same area. Find w.
(2)
Mark scheme · KS3.M-G7 Perimeter and Area of Rectangles and Triangles
Question 1
B1 24 cm cao
Answer: 24 cm
Question 2
B1 24 cm cao
Answer: 24 cm
Question 3
B1 20 cm cao
Answer: 20 cm
Question 4
B1 24 cm2 cao
Answer: 24 cm2
Question 5
B1 20 cm2 cao
Answer: 20 cm2
Question 6
M1 areas of each rectangle found or combined method: 6x4 and 3x4 attempted
A1 36 cm2 cao (24 + 12 = 36)
Answer: 36 cm2
Question 7
M1 use 2(length + width) = 30 or equivalent method to form equation
A1 length = 9 cm cao
Answer: 9 cm
Question 8
B1 10 cm cao
Answer: 10 cm
Question 9
M1 new area computed as 7x7 = 49 or difference method used
A1 increase = 14 cm2 cao (from 35 to 49)
Answer: 14 cm2
Question 10
M1 use area = 1/2 x base x height to form 30 = 1/2 x 5 x h
A1 h = 12 cm cao
Answer: 12 cm
Question 11
M1 area of rectangle and triangle found: 8x3 and 1/2x4x3
A1 total = 30 cm2 cao (24 + 6 = 30)
Answer: 30 cm2
Question 12
B1 24 cm2 cao (1/2 x 6 x 8)
Answer: 24 cm2
Question 13
M1 outline lengths identified correctly, or perimeter of A plus perimeter of B minus twice the joined 4 cm edge (20 + 14 - 8)
A1 26 cm cao
Answer: 26 cm
Question 14
B1 7 cm cao
Answer: 7 cm
Question 15
B1 9 cm cao
Answer: 9 cm
Question 16
M1 area of rectangle and area of triangle found: 12x8 and 1/2x6x4
A1 remaining area = 84 m2 cao (96 - 12 = 84)
Answer: 84 m2
Question 17
M1 subtract rectangle area from total to get triangle area: 100 - 42 = 58
M1 use area = 1/2 x base x height to form 58 = 1/2 x b x 5
A1 b = 23.2 cm cao
Answer: 23.2 cm
Question 18
M1 use rectangle area = length x width and equate to 30