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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

Respuesta :

semsee45

Answer:

105 cm²

Step-by-step 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

[tex]\implies \sf Area=\dfrac12\cdot42\cdot5=105\:cm^2[/tex]

Looking like trapezoid

area:-

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