Question

From a point in the interior of an equilateral triangle perpendiculars are drawn on 3 sides. The length of perpendiculars = 14 cm, 10 cm and 6 cm. Find area

Answer 1

let the sides of equilateral triangle be a

now if we divide the triangle from the point to the vertices

we get three triangle

now

area of 1st triangle= 14/2 × a

                             = 7a

area of 2nd triangle= 10/2 × a

                             = 5a

area of 3rd triangle= 6/2 × a

                             = 3a

total area = 15a

now we know

area of  equilateral triangle =√3/4a²

15a = √3/4a²

15×4/√3=a

a = 5√3

again

area of  equilateral triangle =√3/4a²

                                              =√3/4(5√3)²

                                              =75√3/4 cm²

                                              =32.4 ²cm

Answer 2

to find the area we can use herons formula  

      √s(s-a)(s-b)(s-c)

    s=14+10+6/2

=15

Area=√15(15-14)(15-10)(15-6)

=√15*1*5*9

=√3*5*5*3*3

=3*5√3

area=15√3cm²