Area of figure created by geomitrical shapes

Geometry Level 1

In the figure, a circle of radius 10cm is inscribed within a square. Find the area of the shaded region. (Take pi=3.14)


The answer is 43.

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2 solutions

Anuj Shikarkhane
Jul 25, 2015

Radius of the circle = 10 10 cm

Side of the square = 20 20 cm. ( 10 × 2 ) 10 \times 2)

\therefore Area of square = 20 × 20 = 400 20 \times 20 = 400 sq.cm

Area of the circle = π × r 2 \pi \times r^2 = 3.14 × 100 = 314 = 3.14 \times 100 = 314 sq.cm

Area of square - Area of circle = 400 314 400 - 314

= 86 = 86 sq.cm . This is the area of the 4 4 leftover parts and the area of the 4 4 parts is equal.

\therefore Area of the shaded part = 86 2 = 43 \dfrac{86}{2} = 43 sq.cm

(Upvote if you are satisfied)

well done friend!

Dinamani Borah - 5 years, 10 months ago

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Thank You!

Anuj Shikarkhane - 5 years, 10 months ago

Area of the shaded portion is area of the square minus the area of the circle, then divide the result by two. We have

A = 2 0 2 ( 3.14 ) ( 1 0 2 ) 2 = A=\dfrac{20^2-(3.14)(10^2)}{2}= 43 \color{#D61F06}\boxed{43}

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