A rectangle has length 9 cm and width 4 cm. Write down its perimeter.
(1)
2
A square has side length 11 cm. Calculate its perimeter.
(1)
3
A triangle has sides 6 cm, 9 cm and 10 cm. Work out its perimeter.
(1)
4
Calculate the area of a rectangle with length 8 cm and width 5 cm.
(2)
5
A triangle has base 10 cm and height 6 cm. Calculate its area.
(1)
6
Two rectangles are joined along a side. Rectangle A is 7 cm by 5 cm. Rectangle B is 4 cm by 5 cm. Calculate the total area of the combined shape.
(2)
7
A rectangle has width 8 cm. Its perimeter is 34 cm. Work out the length of the rectangle.
(1)
8
The perimeter of a triangle is 32 cm. Two sides are 11 cm and 12 cm. Find the length of the third side.
(2)
9
A rectangle measures 6 cm by 9 cm. Its length is increased by 3 cm while the width stays the same. Calculate the new area.
(2)
10
A triangle has base 7 cm and area 42 cm2. Work out the height of the triangle.
(2)
11
A shape is made from a rectangle and a triangle. The rectangle is 9 cm by 4 cm. A triangle with base 6 cm and height 5 cm is attached to one side of the rectangle. Calculate the total area of the shape.
(2)
12
A right-angled triangle has legs of length 7 cm and 10 cm. Calculate its area, showing your method.
(2)
13
A rectangle has length 14 cm and area 98 cm2. Work out its width.
(2)
14
A rectangle has perimeter 64 cm. Its length is three times its width. Work out the area of the rectangle.
(3)
15
A triangular flag has a base 3 cm longer than its height. Its area is 44 cm2. Given the height is h cm, form an equation in h, and hence find the height and base of the flag.
(3)
16
A composite shape is made of a rectangle of area 54 cm2 (length 9 cm) and a triangle with height 6 cm attached to one 9 cm side. The total area of the shape is 90 cm2. Work out the base of the triangle.
(3)
17
A rectangular garden is 15 m by 10 m. A triangular flower bed with base 8 m and height 5 m is removed from one corner. Work out the remaining area of the garden.
(3)
18
A triangle has base 9 cm and height 16 cm, so its area is 72 cm2. A rectangle has length 12 cm and unknown width w. The rectangle and the triangle have equal areas. Work out w.
(3)
19
Stretch question. An L-shape is made from an 18 cm by 14 cm rectangle with a 7 cm by 6 cm rectangular notch removed from one corner. Work out the area of the L-shape. Given that the perimeter of the L-shape is 64 cm, work out how much longer this perimeter is compared with the perimeter of the original 18 cm by 14 cm rectangle before the notch was removed.
(4)
Mark scheme · KS3.M-G7D Perimeter and Area of Rectangles and Triangles: Fluency and Exam Drill
Question 1
B1 26 cm cao
Answer: 26 cm
Question 2
B1 44 cm cao
Answer: 44 cm
Question 3
B1 25 cm cao
Answer: 25 cm
Question 4
M1 uses area = length x width
A1 40 cm2 cao
Answer: 40 cm2
Question 5
B1 30 cm2 cao
Answer: 30 cm2
Question 6
M1 finds area of each rectangle: 35 cm2 and 20 cm2
A1 55 cm2 cao
Answer: 55 cm2
Question 7
B1 9 cm cao
Answer: 9 cm
Question 8
M1 uses 32 - 11 - 12
A1 9 cm cao
Answer: 9 cm
Question 9
M1 uses new length = 9 + 3 = 12 cm
A1 72 cm2 cao
Answer: 72 cm2
Question 10
M1 uses height = 2 x area / base
A1 12 cm cao
Answer: 12 cm
Question 11
M1 finds rectangle area 36 cm2 and triangle area 15 cm2
A1 51 cm2 cao
Answer: 51 cm2
Question 12
M1 uses area = (7 x 10) / 2
A1 35 cm2 cao
Answer: 35 cm2
Question 13
M1 uses width = area / length
A1 7 cm cao
Answer: 7 cm
Question 14
M1 forms 2(w + 3w) = 64, so 8w = 64
M1 solves w = 8 cm, so length = 24 cm
A1 area = 192 cm2 cao
Answer: 192 cm2
Question 15
M1 forms h(h+3) = 88 (from (h)(h+3)/2 = 44)
M1 solves the equation to give h = 8
A1 height = 8 cm, base = 11 cm cao
Answer: Height 8 cm, base 11 cm
Question 16
M1 finds triangle area = 90 - 54 = 36 cm2
M1 uses base = 2 x 36 / 6
A1 base = 12 cm cao
Answer: 12 cm
Question 17
M1 finds garden area = 150 m2
M1 finds triangle area = 20 m2
A1 remaining area = 130 m2 cao
Answer: 130 m2
Question 18
M1 confirms triangle area = 72 cm2
M1 sets up 12w = 72
A1 w = 6 cm cao
Answer: 6 cm
Question 19
M1 finds the area of the full rectangle = 252 cm2
M1 finds the area of the notch = 42 cm2
A1 area of L-shape = 210 cm2 cao
B1 difference in perimeter = 0 cm (the L-shape has the same perimeter as the original rectangle)
Answer: Area 210 cm2; perimeter is unchanged (difference 0 cm)