Question

From a point interior
of an equilateral triangle
perpendicular's axe
drawn on the three
sides. The length of
the beximo, perpendicut
-lars are 14cm'and
10 cm and 6cm Find
area of the triangle
A​

Answer 1

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From a point in the interior of an equilateral triangle, perpendiculars are drawn on the three sides. The lengths of the perpendiculars are 14 cm, 10 cm and 6 cm. Find the area of the triangle.

Thinking Process

(i) From a interior point a triangle, three triangle will be formed Determine area of each triangle by using the formula = 1/2 (Base x Height).

(ii) Determine the area of an equilateral triangle by using the Heron’s formula i.e.,

(iii) Further, equate the area of triangle by Heron’s formula and the sum of all three triangle. Simplify it to get the side of D. Hence, find area of the triangle.

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Answer 2

Step-by-step explanation:

AABC is an equilateral triangle.

Let ABC be equilateral triangle of side 'a'cm.

Let P be a point in the interior of the AABC. so PQIBC, PRICA and PSLAB

So PS = 14 cm, PQ = 10 cm and PR = 6 cm =

Area of AABC = Area of AAPB + Area of ABPC +

Area of ACPA