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Question

Emma is planting a garden with the dimensions as shown below. She wants to cover the entire surface of the garden with a thin layer of soil, which costs $2 per sq. m. Find the total amount she has to spend on the entire soil.
$

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Solution

To find the area of the garden, divide the given closed figure into three regions as shown below, such that region A represents the right triangle, region B represents the square and region C represents the right triangle.

Area of region A (right triangle):
From the figure, base = 6 m, height = 5 m
So, the area of the region A
=12×base × height
=12×6×5
=3×5
=15 sq. m

Area of region B (square):
From the figure, side length = 5 m
So, the area of the region B
=(side)2
=52
=25 sq. m

Area of region C (right triangle): As region C is similar to region A
So, the area of the region C= the area of the region C
=15 sq. m

Thus, the total area of the closed figure = area of the region A + area of the region B + area of the region C
=15+25+15
=55 sq. m

Given, cost of soil $2 per sq. m.
The total cost of soil = cost of soil per sq. m × area of the figure
=$2×55
=$110

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