The outline of a rectilinear shape has sides, in order, 8 cm, 3 cm, 5 cm, 4 cm, 6 cm, 7 cm, 2 cm and 5 cm. Work out the perimeter of the shape.
A) 32 cm
B) 40 cm
C) 44 cm
D) 36 cm
E) 48 cm
(Total for Question 1 is 1 mark)
2
Two rectangles are joined along a full side. One rectangle measures 5 cm by 4 cm and the other measures 3 cm by 4 cm. What is the area of the combined shape?
A) 32 cm2
B) 20 cm2
C) 40 cm2
D) 24 cm2
E) 12 cm2
(Total for Question 2 is 1 mark)
3
An L-shaped figure is made by removing a 2 cm by 3 cm rectangle from a 7 cm by 5 cm rectangle (the small rectangle is cut from one corner). What is the area of the L-shaped figure?
A) 29 cm2
B) 35 cm2
C) 6 cm2
D) 28 cm2
E) 23 cm2
(Total for Question 3 is 1 mark)
4
A rectilinear shape has seven known side lengths around its perimeter: 3 cm, 6 cm, 4 cm, 5 cm, 2 cm, 8 cm and 7 cm. The total perimeter is 40 cm. What is the length of the missing side?
A) 3 cm
B) 5 cm
C) 7 cm
D) 4 cm
E) 6 cm
(Total for Question 4 is 1 mark)
5
A 6 cm by 4 cm rectangle and a 4 cm by 2 cm rectangle are placed side by side so that their 4 cm sides lie along the same straight line (they are adjacent but do not overlap). What is the area of the combined shape?
A) 32 cm2
B) 24 cm2
C) 20 cm2
D) 30 cm2
E) 16 cm2
(Total for Question 5 is 1 mark)
6
A rectangle measures 9 cm by 6 cm. A small 3 cm by 2 cm rectangle is removed from one corner. What is the area of the remaining shape?
A) 48 cm2
B) 52 cm2
C) 54 cm2
D) 42 cm2
E) 36 cm2
(Total for Question 6 is 1 mark)
7
Two rectangles, 6 cm by 3 cm and 6 cm by 2 cm, are placed one above the other sharing the 6 cm side. What is the total area?
A) 30 cm2
B) 18 cm2
C) 24 cm2
D) 12 cm2
E) 36 cm2
(Total for Question 7 is 1 mark)
8
A rectilinear shape has side lengths around the perimeter: 7 cm, 4 cm, 6 cm, 3 cm, 5 cm and x cm. The total perimeter is 32 cm. What is x?
A) 7 cm
B) 6 cm
C) 5 cm
D) 3 cm
E) 8 cm
(Total for Question 8 is 1 mark)
9
A compound shape is formed by a 10 cm by 4 cm rectangle with a 4 cm by 2 cm rectangle attached to one short end so the 4 cm sides touch. What is the perimeter of the combined shape?
A) 28 cm
B) 30 cm
C) 32 cm
D) 34 cm
E) 36 cm
(Total for Question 9 is 1 mark)
10
A square of side 6 cm has a 2 cm by 3 cm rectangle removed from one side (not a corner) leaving a rectilinear shape. What is the area of the new shape?
A) 30 cm2
B) 36 cm2
C) 33 cm2
D) 24 cm2
E) 18 cm2
(Total for Question 10 is 1 mark)
11
On a plan, a rectilinear shape has side lengths 9 m, 4 m, 5 m, 3 m, 7 m and 6 m in that order. What is the perimeter of this shape in metres?
A) 34 m
B) 36 m
C) 32 m
D) 38 m
E) 30 m
(Total for Question 11 is 1 mark)
12
A rectilinear tile layout consists of a 7 cm by 6 cm rectangle and a 2 cm by 6 cm rectangle placed end to end (sharing the 6 cm side). What is the total area in cm2?
A) 54 cm2
B) 42 cm2
C) 36 cm2
D) 60 cm2
E) 24 cm2
(Total for Question 12 is 1 mark)
13
The perimeter of a rectilinear shape is 54 cm. The side lengths around the shape in order are 8 cm, x cm, 5 cm, 3 cm, 10 cm, 6 cm, 4 cm and 8 cm. Work out the value of x.
(Total for Question 13 is 2 marks)
14
An L-shaped garden is formed by removing a 3 m by 2 m rectangle from a corner of a 9 m by 6 m rectangle. Find the area of the remaining garden.
(Total for Question 14 is 3 marks)
15
Two rectangles, 7 cm by 3 cm and 7 cm by 4 cm, are placed so the 7 cm sides are aligned and the rectangles share that side (they are stacked). Find the perimeter of the combined shape.
(Total for Question 15 is 2 marks)
16
A rectangle measures 10 cm by 6 cm. A 4 cm by 3 cm rectangle is removed from one corner. Find the area of the remaining shape.
(Total for Question 16 is 3 marks)
17
A tiled L-shaped kitchen floor is made from two rectangles: one 5 m by 4 m and the other 3 m by 4 m placed end to end sharing the 4 m side. Calculate the total area of the kitchen floor.
(Total for Question 17 is 2 marks)
18
A rectilinear plot has sides 12 cm, 5 cm, 7 cm, x cm, 4 cm and 9 cm. The perimeter is 54 cm. Find x.
(Total for Question 18 is 3 marks)
19
A building plan shows an 8 m by 6 m rectangle. From one side a 2 m by 3 m rectangle is removed and on another side a 4 m by 2 m rectangle is attached (externally). Find the area of the final shape.
(Total for Question 19 is 3 marks)
20
The perimeter of a rectilinear shape is 70 cm. The side lengths in order are 14 cm, 8 cm, 6 cm, x cm, 10 cm and 12 cm. (a) Find x. (b) The same shape can be split into a rectangle 14 cm by 6 cm and a square 6 cm by 6 cm. Find the total area of the shape.
(a)Find x.(2)
(b)Find the total area using the rectangle 14 x 6 and the square 6 x 6.(2)
(Total for Question 20 is 4 marks)
Mark scheme · EP.M115 Perimeter and Area of Compound Shapes
Answer: A) 7 cm (sum known = 7+4+6+3+5 = 25; 32 - 25 = 7 cm).
Question 9
B1 correct option C (32 cm) cao
Answer: C) 32 cm. (Because the 4 cm sides match exactly, the two rectangles join flush to form one straight rectangle 4 cm by (10+2) = 12 cm. Perimeter = 2 x (4 + 12) = 32 cm.)