Question

find the area of equilateral triangle whose altitude is 16 root 3​

Answer 1

Answer:

256√3 cm²

Step-by-step explanation:

√3/2 × a = 16√3

√3 cancel on both sides.

a/2 = 16

a = 32

All the three sides measure 32 cm

Area of equilateral triangle = √3/4 × a²

= √3/4 × 32 × 32

= 256√3 cm²

Answer 2

Answer :-

Area of the equilateral tiangle is 256√3 units²

Explanation :-

Finding side of an equilateral triangle

Altitude of an equilateral triangle = 16√3 units

Also, Altitude of an equilateral triangle = √3 * ( a/2)

[Where a = Side of the equilateral triangle]

$\mathsf{ \implies16 \sqrt{3} = \dfrac{ \sqrt{3} a}{2} }$

$\mathsf{ \implies \dfrac{16 \sqrt{3} }{ \sqrt{3} } = \dfrac{ a}{2} }$

$\mathsf{ \implies16= \dfrac{ a}{2} }$

$\mathsf{ \implies16 \times 2= a}$

$\mathsf{ \implies 32= a}$

$\mathsf{ \implies a = 32}$

i.e Side of an equilateral triangle = 32 units

Finding the are af the equilateral triangle

Area of the equilateral triangle = (√3/4) * a²

[Where a = Side of the equilateral triangle]

$\mathsf{ = \dfrac{ \sqrt{3} }{4} \times {32}^{2} }$

$\mathsf{ = \dfrac{1024 \sqrt{3} }{4}}$

$\mathsf{ = 256 \sqrt{3}}$

∴ Area of the equilateral tiangle is 256√3 units².