Perimeter of quadrant is 25 cm find its area?

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Answer

Here's ur answer bud,

Perimeter of a quadrant = radius + radius + length of arc

Perimeter of quadrant = r + r + angle/360× 2πr

25 = 2r+ 90/360× 2×22/7×r

25 = 2r+ 11/7r

25 = 25r / 7

r =7

area = 1/4πr^2 = 1/4× 22/7 ×7 ×7 = 38.5 sq.cm

UPvote and lemme know if that helped:))

Answer

Answer

Perimeter of Quadrant:
The perimeter of a quadrant is the sum of the lengths of all its sides. In the case of a quadrant, it refers to one-fourth of the circumference of a circle.

Given:
Perimeter of quadrant = 25 cm

Calculating the Circumference:
To find the area of a quadrant, we first need to calculate the circumference of the whole circle. The circumference of a circle can be calculated using the formula:

Circumference = 2πr

Since a quadrant is one-fourth of a circle, the radius of the quadrant will be half of the radius of the whole circle. Let's assume the radius of the whole circle is 'r'. Therefore, the radius of the quadrant will be 'r/2'.

Calculating the Perimeter of the Quadrant:
Since the perimeter of the quadrant is one-fourth of the circumference, we can calculate it by dividing the circumference by 4:

Perimeter of quadrant = Circumference / 4

Substituting the formula for circumference, we get:

Perimeter of quadrant = (2πr) / 4

Simplifying the equation, we have:

Perimeter of quadrant = πr / 2

Given Perimeter:
We are given that the perimeter of the quadrant is 25 cm. Therefore, we can write the equation as:

25 = πr / 2

Calculating the Radius:
To find the radius, we rearrange the equation:

πr = 25 * 2

πr = 50

r = 50 / π

Calculating the Area of the Quadrant:
To find the area of the quadrant, we can use the formula:

Area of quadrant = (πr²) / 4

Substituting the value of r, we get:

Area of quadrant = (π * (50 / π)²) / 4

Simplifying the equation, we have:

Area of quadrant = (2500 / π) / 4

Area of quadrant = 625 / π

Therefore, the area of the quadrant is 625 / π square units.

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Similar Class 10 Doubts

THE AREA OF A CIRCLE INSCRIBED IN AN EQUILATERAL TRIANGLE IS 154 CM SQ. .THEN FIND THE PERIMETER OF TRIANGLE.USE PI AS 22/7 AND ROOT 3 AS 1.73?

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