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.
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Answer:
24 cm²
Step-by-step explanation:
Let say Tangents length are a , b , c , d to the vertex of Quadrilateral to respective Tangent points (point touching circle)
Total 8 Triangles will be formed
Area of Each Triangle = (1/2) ( vertex of Quadrilateral to respective Tangent points) * Radius
= (1/2) ( a + a + b + b + c + c + d + d) * Radius
= (a + b + c + d) * Radius
a + b + c + d = Sum of two opposite sides of Quadrilateral = 12 cm
Radius = 2 cm
Area = 12 * 2 = 24 cm²
or Simply we can say
Area = Semi Perimeter * Inner Radius
Semi perimeter = Sum of two opposite sides = 12 cm
Inner Radius = 2 cm
Area = 12 * 2 = 24 cm²
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