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Question

# Calculate the areas of the shapes below:

Solution

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a)

The shape consists of a square of side length $8$ cm, and $4$ congruent triangles, each of base length $8$ cm and height $4$ cm.

Area of square of side length $l$ cm is $l^2\ \text{cm}^2$

$=8^2=\color{#4257b2}64\ \text{cm}^2$

Area of triangle of base length $b$ and height length $h$ is $\frac{1}{2}bh$

$=\frac{1}{2}\times 8 \times 4=\color{#4257b2}16\ \text{cm}^2$

Total area = area of square + $4\times$ area of triangle

$=64+4\times 16=\color{#4257b2}128\ \text{cm}^2$

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