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A square 10cm on each side has four quarter circles drawn with centers at the four corners. How many square centimeters are in the area of the shaded region? Express your answer in terms of $\pi$.

A square 10cm on each side has four quarter circles drawn with centers at the four-example-1
User Kroid
by
6.1k points

2 Answers

14 votes

Answer:The answer is 100-25pi

Explanation:

quarter circles = full circle

Full circle area = pie r2

Square area = s2

In this case, the side of the square is twice the radius of the circle

User Ruyk
by
6.0k points
4 votes

Area of shaded region in term of π is 100-25π.

How to calculate the area of the shaded region.

A quarter circle is a curve or arc that spans one-fourth (1/4) of the circumference of a full circle. In terms of degrees, a quarter circle represents 90 degrees since there are 360 degrees in a complete circle, and 360 divided by 4 equals 90.

Area of square = s²

where

s is length of the side of square

r radius of the circles

r = s/2

= 10/2 = 5

Four quarter circles = 1 full circle

Area of the shaded region= area of square - area of circle.

area of circle = πr²

Area of shaded region = 10² - π(5)²

= 100-25π

Therefore, area of shaded region in term of π is 100-25π

User Gaurav Pant
by
4.8k points
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