Area

Geometry Level 3

The above shows a figure drawn on a unit grid. What is the area of the shaded region?


The answer is 33.

A Former Brilliant Member by A Former Brilliant Member

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2 solutions

The area of the shaded region = the area of the large square − the area of the non-shaded region A = 7 2 − ( 3 + 2 + 1 + 2 + 6 + 2 ) = 49 − 16 = 33 \begin{aligned} \text{The area of the shaded region } & = \text{ the area of the large square } - \text{ the area of the non-shaded region} \\ A & = 7^2 - (3+2+1+2+6+2) \\ & = 49-16 \\ & = \boxed{33} \end{aligned}

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area of shaded region \text{area of shaded region} = 7 2 − 1 2 ( 2 ) ( 3 ) − 1 2 ( 1 ) ( 4 ) ( 3 ) − 1 ( 1 ) − 1 2 ( 2 ) ( 6 ) = 33 = 7^2 - \frac{1}{2}(2)(3) - \frac{1}{2}(1)(4)(3) - 1(1) - \frac{1}{2}(2)(6) = 33 square units \text{square units}

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Easy does it

Peter van der Linden - 4 years, 2 months ago

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