If the height of an equilateral triangle is 20√2 cm, then what is its area (in cm2)?
Show answer & explanation
Correct answer: C
Explanation
Correct Answer is option 3 i.e. 1/3(800√3)
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Understanding |
Application |
Calculation |
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Suppose side of equilateral triangle = x |
We know that: Height = √(x2 – x2/4) Height = x√3/2 cm |
√(x2 – x2/4) ⇒ √(3x2/4) ⇒ x√3/2 |
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Height of equilateral triangle = 20√2 cm |
So, x√3/2 = 20√2 ⇒ x = 40√2/√3 cm |
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We know that: Area of Equilateral triangle = √3/4 × x2
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So, Area = 1/3(800√3) cm2 |
⇒ √3/4 × (40√2/√3)2 ⇒ √3/4 × 3200/3 ⇒ 1/3(800√3) |