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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Answer 1

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 $A$
$=\frac{1}{2}\times \text{base}\times \text{height}$
$=\frac{1}{2}\times 6\times 5$
$=3\times 5$
$=15$ sq. m

Area of region B (square):
From the figure, side length = 5 m
So, the area of the region $B$
$={\text{(side)}}^2$
$=5^2$
$=25$ 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
$=\$2\times 55$
$=\$110$