a house

Geometry Level 1

A young boy drew the front elevation of a house and put the dimensions as shown. He colored the windows with red, the door with purple, the wall with blue, the wall below the roof with green and the circle design with yellow. What is the sum of the areas of the green region and the blue region in square meters? (pi=3.14) Give your answer until four decimal places.

Note: All shapes shown above are triangle, rectangle and circle.


The answer is 11.3274.

A Former Brilliant Member by A Former Brilliant Member

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1 solution

Well this is basic geometry. The area of the green region is equal to the area of the triangle minus the area of the circle. And it is 1 2 ( 1.5 ) ( 4 ) − 3.14 ( 0.3 ) 2 = 2.7174 \dfrac{1}{2}(1.5)(4)-3.14(0.3)^2=2.7174 . The area of the blue region is equal to the of the wall minus the areas of the two windows and minus the area of the door. And it is 3 ( 4 ) − 1.2 ( 1 ) − 0.9 ( 2.1 ) − 0.3 ( 1 ) = 8.61 3(4)-1.2(1)-0.9(2.1)-0.3(1)=8.61 . So the sum that we are looking for is 2.7174 + 8.61 = 11.3274 square meters \color{#D61F06}\boxed{2.7174+8.61=11.3274~\text{square meters}} .

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