Question

In the following figure, OE = 20 cm. In sector OSFT, square OEFG is inscribed. Find the area of the shaded region.​

Answer 1

Answer:

The area of shaded region is 228 cm².

Step-by-step explanation:

GIVEN :

OEFG is a square , OE = 20 cm  

In the figure join OF

OF is the diagonal of a square.

Diagonal of a square = √2 × side

= √2 × 20

Diagonal of a square = 20√2 cm

Radius of circle,r = Diagonal of a square = 20√2 cm

Radius of circle,r  = 20√2 cm

Area of quadrant, OTFB  = ¼ × πr²

= ¼ × 3.14 × (20√2)²

= ¼ × 3.14 × 400 × 2

= (100 × 6.28

= 628 cm²

Area of quadrant, OTFB = 628 cm²

Area of square, OEFG = Side² = 20² = 400 cm²

Area of shaded region  = Area of quadrant ,OTFB  - Area of square,OEFG

= 628 - 400

= 228 cm²

Area of shaded region = 228 cm²

Hence,the area of shaded region is 228 cm².

HOPE THIS ANSWER WILL HELP YOU….

Here are more questions of the same chapter :

In the following figure, OABC is a square of side 7 cm. If OAPC is a quadrant of a circle with centre O, then find the area of the shaded region. (Use $(\pi=\frac{22}{7})$)

https://brainly.in/question/9487448

In the following figure a square OABC is inscribed in a quadrant OPBQ of a circle. If OA = 21 cm, find the area of the shaded region.

https://brainly.in/question/9484955

Answer 2

Answer:

228.5cm²

Step-by-step explanation:

It’s seen that, OEFG is a square of side 20 cm.

So its diagonal = √2 side = 20√2 cm

And, the radius of the quadrant = diagonal of the square

Radius of the quadrant = 20√2 cm

So, Area of the shaded portion = Area of quadrant – Area of square

= 1/4 πr² – side²

= 1/4 (22/7)(20√2)² – (20)²

= 1/4 (22/7)(800) – 400

= 400 x 4/7

= 1600/7

= 228.5 cm²