The answers are Radius of circle 5 cm
Area of Quadrilateral = 20 cm²
Given: Bottom side of the quadrilateral is diameter of the circle
From given picture bottom of the quadrilateral AB = 10cm
and CD = 6 cm
To find: Radius of the circle and area of the quadrilateral
Solution:
a) Radius of circle
given that diameter of circle = bottom of quadrilateral
⇒ diameter of circle 2r = 10 cm
⇒ Radius of circle r = 10/2 = 5 cm
∴ Radius of circle 5 cm
b) Area of the quadrilateral
Draw a line by joining mid points of AB and CD
and join mid point of AB and vertice C then a right angle triangle POC is formed as show figure
In triangle POC ⇒ OC² = OP²+ PC²
[ here OC = radius = 5 cm and PC = [tex]\frac{1}{2} (CD)[/tex] = 3 cm ]
⇒ 5 ² = OP²+ 3²
⇒ OP² = 5² - 3² = 25 - 9 = 16
⇒ OP² = 4²
⇒ OP = 4 is the altitude/height of trapezium
Therefore, area of trapezium = [tex]\frac{1}{2} (base)(height)[/tex]
⇒ [tex]\frac{1}{2} (10)(4)[/tex] = 5(4) = 20 cm²
∴ Area of triangle = 20 cm²
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