Question

A quadrilateral is circumscribed about a circle. The sum of the lengths of its two opposite sides is 21 cm, and the radius of the circle is 5 cm. Find the area of the quadrilateral.

I will give 100 points

Answer 1

Looking like trapezoid

area:-

• 1/2(sum of parallel sides)(Height)
• 1/2(21+21)(5)
• 1/2(42)(5)
• 21(5)
• 105cm²

Answer 2

105 cm²

Explanation:

Properties of a quadrilateral circumscribed about a circle

• Each side of the quadrilateral is a tangent to the circle.
• The sums of the measures of the opposite sides of the quadrilateral are equal.
• The area of the quadrilateral is half the product of its perimeter and the radius of the circle.

Given:

• Radius = 5 cm
• Sum of the lengths of its two opposite sides = 21 cm

Therefore, the sum of the other pair of opposites is also 21 cm.

So the perimeter = 21 + 21 = 42 cm

`\implies \sf Area=\frac12\cdot42\cdot5=105\:cm^2`