Mathematics
In the figure (i) given below, ABC is an equilateral triangle with each side of length 10 cm. In △BCD, ∠D = 90° and CD = 6 cm. Find the area of the shaded region. Give your answer correct to one decimal place.
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Answer
Given,
ABC is an equilateral triangle of side = 10 cm
We know that,
Area of equilateral triangle ABC =
Substituting the values we get,
In right angled triangle BCD,
⇒ BC2 = BD2 + CD2
⇒ 102 = BD2 + 62
⇒ BD2 = 100 - 36
⇒ BD2 = 64
⇒ BD = 8 cm.
We know that,
Area of right angled triangle = × base × height.
Area of △BCD = = 24 cm2
From figure,
Area of shaded portion = Area of triangle ABC - Area of triangle BCD
Substituting the values we get,
Area of shaded portion = 43.3 - 24 = 19.3 cm2.
Hence, area of shaded region = 19.3 cm2.
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