Mathematics
In the figure (ii) given below, ABC is an isosceles right angled triangle with ∠ABC = 90°. A semicircle is drawn with AC as diameter. If AB = BC = 7 cm, find the area of the shaded region. Take π = .
![In the figure, ABC is an isosceles right angled triangle with ∠ABC = 90°. A semicircle is drawn with AC as diameter. If AB = BC = 7 cm, find the area of the shaded region. Mensuration, ML Aggarwal Understanding Mathematics Solutions ICSE Class 9.](https://cdn1.knowledgeboat.com/img/mla9/q24b-c16-ex-16-3-mensuration-ml-aggarwal-solutions-icse-class-9-649x679.png)
Mensuration
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Answer
By formula,
Area of △ABC = × base × height
= × BC × AB
= × 7 × 7
= = 24.5 cm2.
In right angle triangle,
Using pythagoras theorem,
⇒ AC2 = AB2 + BC2
⇒ AC2 = 72 + 72
⇒ AC2 = 49 + 49 = 98
⇒ AC = cm.
From figure,
Radius of semi-circle (r) =
By formula,
Area of semi-circle =
Area of the shaded region = Area of the semi-circle – Area of △ABC
= 38.5 - 24.5
= 14 cm2.
Hence, area of the shaded region = 14 cm2.
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