Question

Find the area of the shaded region in the following figures....​

Answer 1

Answer:

Area of shaded part is 456cm²

Step-by-step explanation:

Here in figure we have a circle in which one square is present and need to find the area which is shaded.

To find the area which is shaded first we need to find area of square and area of circle than subtract area of square from the area of circle.

As in question its also mention be can use area of square $=\frac{1}{2}(diagonal)^{2}$

Diagonal of square = 40 cm

Area of square $=\frac{1}{2}(diagonal)^{2}=\frac{1}{2}(40)^{2}=\frac{1}{2}(1600)=800$

Area of square $=800cm^2$

By the figure we can see diagonal of square = Diameter of circle = 40 cm

Radius of circle =$\frac{diameter}{2}= \frac{40}{2} = 20 cm$

Area of circle = πr²=3.14 × (20)² = 3.14 x 400 = 1256 cm²

Area of shaded part = Area of circle - Area of square

= 1256cm² - 800cm²  = 456 cm²

Answer 2

Step-by-step explanation:

To find the area of the shaded region:

1. Find the area of the square
2. Find the area of the circle
3. Subtract the area of the square from the area of the circle.

1) Area of square

Let the side of the square be "x"

Diagonal SQ = 40 cm

To find the length of the sides of a square,

Let's take the triangle SRQ right at R,

By Pythagoras Theorem:

The square of hypotenuse = sum of the squares of the legs.

(Eq1)

$40^{2} = x^{2} + x^{2} \\ 1600 = 2x^{2} \\\frac{1600}{2} = x^{2} \\ 800 = x^{2}$

Let's take the side of the square as "x"

Area of the square = $side^{2} = x^{2}$

Area of the square $x^{2} = 800$        (By Eq1)

Area of the square = 800 sq. cm.

2) Area of a circle

Area of a circle = π$r^{2}$

Diameter of a circle = Diagonal SQ of a square

Diagonal = 40 cm = Diameter

Radius = $\frac{Diameter}{2} = \frac{40}{2} = 20cm$

Area of the circle π$r^{2}$ = π x 20 x 20 = 400π sq. cm.

Area of the circle = 400π sq. cm.

3) Area of the shaded region.

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

                                            = 400π - 800 sq. un

Answer:

Area of the shaded region = 400π - 800 sq. units

(HOPE THIS HELPS YOU FOR ANSWERING MORE TYPES OF THIS QUESTION, AND HOPE YOU MAKE IT AS BRAINEIST)