Question

A square is inscribed in a circle of radius 14cm. Calculate the area outside the square but inside the circle?

Answer 1

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Answer 2

The answer is 224 cm²

Given: A square is inscribed in a circle

Radius of the circle r = 14 cm

To find: Measurement of area outside the square but inside the circle

Solution:

Area outside the square = area of circle - area of square

Now find area of circle and square

⇒ Area of circle = π r² = $(\frac{22}{7} )(14)(14)$ = 22(2)(14) = 616 cm²

When a square inscribed in circle the diameter of circle will be equal to the diagonal of square

As we know diagonal of a square = $\sqrt{2} a$  where a is side

And diameter of circle d = 2r

⇒  $\sqrt{2} a = 2r$  

⇒  $a = \frac{2r}{\sqrt{2} }$  

⇒  $a = \frac{\sqrt{2} \sqrt{2} r}{\sqrt{2} }$ = $\sqrt{2} r$  

Side of square a = $\sqrt{2} (14)$ = 14√2  [ from data r = 14 ]

⇒ Area of square = (side)² = (14√2)² =  196 × 2 = 392 cm²

Therefore, area outside the square = 616 cm² - 392 cm²  = 224 cm²

Measurement of area outside the square = 224 cm²

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