Question

In figure, ABCD is a

square of side 28cm. With

centers A, B, C and D each

circle touch externally two

of the remaining three

circles. Find the area of

the shaded region.​

Answer 1

Question:-

In figure, ABCD is a square of side 28cm. With centers A, B, C and D each circle touch externally two of the remaining three circles. Find the area of the shaded region.

Answer:-

Given,

– ABCD = Square

– One side of a square = 28 cm.

– Radius of circles with centre A, B, C, and D = 14 cm.

To find,

Area of the shaded region

Solution,

Area of Shaded region

= Area of square - Area of four 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 14 cm radius. So, Area of four sectors will be equal to Area of one complete Circle.

→ Area of Square = (side)² sq.units

= 28²

= 784 cm²

→ Area of 4 sectors = πr²

= 22/7 × 14 × 14

= 22 × 2 × 14

= 616 cm²

We have found all the required measures. So, we can proceed with the next step, finding the area of shaded region. As before we have calculated that the area of shaded region is Area of square (ABCD) - area of 4 sectors (a circle)

= 784 - 616

= 168 cm²

Therefore, the area of Shaded region = 168 cm².

____________________

Answer 2

Step-by-step explanation:

Given:In figure, ABCD is a square of side 28cm. With centers A, B, C and D each circle touch externally two of the remaining three circles.

To find: Find the area of the shaded region.

Solution:

It is clearly visible that all circles are equal( because all have same radius).

4 quadrant of 4 equal circles forms one complete circle.

Thus,

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

Step 1: Find Area of square.

We know that area of square=$( {side)}^{2}$

Side= 28 cm

Area$= 28 \times 28$

Area of square $\bf = 784 \: {cm}^{2}$

Step 2: Find Area of circle.

We know that area of circle is given by $= \pi \: {r}^{2}$

r=14 cm

Area of circle$= \frac{22}{7} \times 14 \times 14$

Area of circle$= 22 \times 2 \times 14$

Area of circle$\bf = 616 \: {cm}^{2}$

Step 3: Area of shaded region.

Area of shaded region$= 784 - 616$

Area of shaded region$\bf = 168 \: {cm}^{2}$

Final answer:

Area of shaded region is 168 cm².

Hope it will help you.

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