Question

From a point in Interior of equilateral triangle. Perpendicular are drawn to 3 sides of length
10cm,6cm,14cm.Find area of equilateral Triangle
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Answer 1

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Answer 2

Answer:

Hence, the area of triangle = 12a = 192 √3 = 332.55 cm²

Step-by-step explanation:

Let the equilateral triangle ∆ABC is of side ‘a’ and the interior point is P. So the area of triangle will be the sum of ∆APB, ∆BPC, and ∆CPA. Now, since the perpendicular to the 3 sides are 6, 8, and 10, hence -

Area of ∆ABC = 1/2 * 6 * a + 1/2 * 8 *a + 1/2 * 10 * a = 3a + 4a + 5a = 12a

Also, since ∆ABC is an equilateral triangle of side ‘a’, its area would be √3 * a²/4

Hence, √3 * a²/4 = 12 a

or, √3 * a/4 = 12

or, a = 12 * 4 / √3 = 16 √3

Hence, the area of triangle = 12a = 192 √3 = 332.55 cm²