The area of the shape is 2070 m²
The perimeter of the shape is 210.43m
Calculating Perimeter and Area
From the question, we are to determine the area and perimeter of the shape
The given shape is a trapezium
The area of a trapezium is given by the formula,
A = 1/2(a+b)h
Where A is the area
a and b are the parallel sides
h is the height
In the given diagram,
a = 54m
b = 54m + 30m = 84m
h = 30m
∴ A = 1/2(54 + 84) × 30
A = 1/2(138) × 30
A = 69 × 30
A = 2070 m²
Hence, the area of the shape is 2070 m²
To calculate the perimeter (distance around the shape)
First, we will determine the slant height, x
x² = 30² + 30² (Pythagorean theorem)
x² = 900 + 900
x² = 1800
x = √1800
x = 42.43 m
Now,
The perimeter of the trapezium is
P = 30m + 54m + 30m + 42.43m + 54m
P = 210.43m
Hence, the perimeter of the shape is 210.43m
Learn more on Calculating area and perimeter here: https://brainly.com/question/26900809
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