Question

The height of an equilateral triangle measure 9 cm find its area correct to 2 place are decimal (take root 3 = 1.73

Answer 1

we know that area of a triangle is 1/2×b×h
moreover in equilatrai triangle area is (√3/4)×side²
now equating both equations, we get
1/2×b×h=(√3/4)side²
base is equal to side in equilatral∆
1/2×side× h=√3/4×side²
h=√3/2×side
9=√3/2×side
side=6√3
Area=1/2×b×h
1/2×6√3×9
area=27√3
=46.71

Answer 2

Answer:

Consider a as the side of an equilateral triangle We know that Height of an equilateral triangle = √3/2 a

It is given that height = 9cm So we get √3/2 a = 9

On further calculation a = (9 × 2)/ √3

Multiplying both numerator and denominator by √3 We get

a = (9 × 2 × √3) / (√3 × √3)

So we get Base = a = 6√3cm

We know that the area of an equilateral triangle = ½ × b × h

By substituting the values Area of the equilateral triangle = ½ × 6√3 × 9

On further calculation Area of the equilateral triangle = 27√3 cm2

By substituting the value of √3

Area of the equilateral triangle

= 27 × 1.732 = 46.764

By correcting to 2 places of decimal Area of the equilateral triangle = 46.76 cm2

Therefore, the area of an equilateral triangle = 46.76 cm2.