Question

1) The sum of the lengths of two opposite sides of the circumscribed quadrilateral is 12 cm, the length of a radius of the circle is 2 cm. Find the area of the quadrilateral.

2) A quadrilateral is circumscribed around a circle. The sum of the lengths of two of its opposite sides is 15 cm. Find the perimeter of the quadrilateral.

Answer 1

24cm and 225cm

Explanation:

Answer 2

1)
`24cm^2`

2)
`30cm`

Explanation:

1) Remember that: The area of a quadrilateral circumscribed about a circle equals semi-perimeter (half the product of the perimeter of the quadrilateral) and the radius of the circle.

By the other hand in a quadrilateral circumscribed the sum of the measures of any pair of two opposite sides is equal to the sum of the measures of the other pair of the opposite sides.

Then you know that the sum of all sides should be 12cm+12cm=24cm

Area= Semi-perimeter*r

where

Semi-perimeter= perimeter/2= sum of all sides/2

r= radius of the circle

Then:

`Area=(24cm/2)*(2cm)= 24cm^2`

2) Perimeter= sum of all sides

And as the sum of the measures of any pair of two opposite sides is equal to the sum of the measures of the other pair of the opposite sides.

Perimeter=15cm+15cm=30cm