Question

ABCD is a square of side 14 centimetre from each corner of the square A quadrant of a circle of radius 3.5 cm and also a circle of radius 4 cm is cut as shown in the figure find the area of remaining shaded portion of square​

Answer 1

Given,

Side of a square ABCD=14cm

Radius of circles with centers A,B,C and D=14/2=7cm

Area of Shaded region= Area of square-Area of 4 sectors subtending right angle.

Area of each of the 4 sectors is equal to each other and is a sector of 90° in a circle of 7 cm radius. So, Area of four sectors will be equal to Area of one complete circle.

Now refer the attachment...

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Answer 2

area of the remaining shaded portion is  107.21 cm ²

Step-by-step explanation:

area of the remaining shaded portion = area of square - area of middle circle - area of 4 quadrants

for square ABCD

area of square = side ²

side = 14 cm

area of square = 14² = 196 cm ²

area of middle circle :

radius of circle = 4 cm

area of circle = $\pi r^2$

= $\frac{22}{7} \times 4\times 4 = \frac{352}{7} = 50.29 cm^2$

for quadrant

area of 1 quadrant = $\frac{1}{4} \pi r^2$

radius of quadrant of circle = 3.5 cm

then area of 4 quadrant = $4\times \frac{1}{4} \pi r^2= \pi r^2$

area of 4 quadrant = $\frac{22}{7}\times 3.5\times 3.5$

= 38.5 cm²

then

area of the remaining shaded portion = area of square - area of middle circle - area of 4 quadrants

area of the remaining shaded portion = 196-(50.29+38.5)

area of the remaining shaded portion = 107.21 cm ²

hence , area of the remaining shaded portion is  107.21 cm ²

#Learn more:

From each corner of a square of side 4 centimetre a quadrant of a circle of radius 1 cm is cut and also circle of diameter 2 cm is cut find the area of remaining portion of the square

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