Question 1
A diagram of the ground floor of a house is shown in the diagram below.
Use the diagram below to calculate the perimeter of the ground floor.
Select the correct answer from the list below:
Correct: 34
B: 33
C: 36
D:42
WORKED SOLUTION:
The missing side of the living room is 5 m and the missing side of the bathroom is 3 m.
The total of the bottom is 3+2+5=9 m
The total of the top is 3+4=7 m
The missing part on the top of the bathroom is 9-7=2 m
The total perimeter is 3 + 5+ 7 + 5 + 2 + 3 + 9 = 34 m
Question 2
Shape ABCD is shown below.
Calculate the perimeter of shape ABCD
Select the correct answer from the list below:
Correct: 240 m
B: 120 m
C: 220 m
D: 260 m
WORKED SOLUTION:
AD is the same length as BC, so AD = BC = 20 m
AB is the same length as CD, so AB = CD = 100 m
The total perimeter is 100 + 20 + 100 + 20 = 240 m
Question 3
The diagram of a floor plan is shown below.
AB = 100 m
Using the diagram below, calculate the perimeter of the floor.
Select the correct answer from the list below:
Correct: 265 m
B: 295 m
C: 280 m
D: 240 m
WORKED SOLUTION:
We add up all side lengths.
Perimeter = 100 + 45 + 15 + 80 + 15 + 10 = 265 m
Question 4
The shape below is made by attaching two semicircles to a rectangle 25 cm long.
The radius of the semi circles are 15 cm long.
Find the perimeter of the shape, to 2 decimal places.
Select the correct answer from the list below:
Correct: 144.25 cm
B: 238.50 cm
C: 97.12 cm
D: 119.25 cm
WORKED SOLUTION:
To work out the length of one of the semi circles at the end, we use the circumference formula for a circle: \pi d or 2 \pi r
However, we need the circumference of a semi circle, so we need to half this formula: \frac{1}{2} \pi d or \pi r
Therefore, the circumference of one of the semi circles is \pi \times 15 = 47.1238...
Hence, the total perimeter is 25 + 25 + 47.1238... + 47.1238... = 144.2477... = 144.25 (2 dp)
Question 5
The shape below is made from attaching 5 different sized rectangles together.
Calculate the perimeter of the shape formed.
Select the correct answer from the list below:
Correct: 42 m
B: 32 m
C: 37 m
D: 41 m
WORKED SOLUTION:
Missing side lengths for shape 1 are 5 m and 5 m.
Missing side length for shape 3 is 1 m.
Missing side length for shape 4 is 3 m.
Missing side lengths for shape 5 are 5 m, 2 m and 5 m.
Therefore, the perimeter is 3+5+5+5+1+5+2+5+3+2+1+5=42 m