Question

the height of an equilateral triangle measurs 12 cm. Find the area of triangle correct to 2 places of decimal​. (use$\sqrt{3}$as 1.732)

Answer 1

Answer :

80.24m^2

Step-by-step explanation:

hope this helps

thank you

Answer 2

Answer:

$339.48cm^2$

Explanation:

Figure :

$\setlength{\unitlength}{20} \begin{picture}(6, 6) \put(2, 2){\line(1, 0){8}}\put(6, 2){\line(0, 1){4}}\put(2, 2){\line(1, 1){4}}\put(10, 2){\line( - 1, 1){4}}\put(5.6,1.5 ){ \bf a }\put(3,4 ){ \bf a }\put(8.5,4 ){ \bf a }\put(6.2, 3.5){ \bf h }\put(2, 1.5){ \bf A }\put(10, 1.5){ \bf B }\put(6,6 ){ \bf C }\put(3, 0) {\bf {}}\end{picture}$

Given :

• Height of the equilateral triangle.

To Find :

• Area of triangle correct to 2 places of decimal​.

Solution :

Height(h) => 12cm

The height is perpendicular to the side AB and it divides it in two halves, which are a2 long.

Use Pythagorean therom here

$\implies a^{2} =12^{2}+\bigg(\dfrac{\ a^{2}}{2}\bigg)$

$\implies a^{2}=144+\dfrac{\ a^{2}}{2}$

$\implies \dfrac{4a^{2}-a^{2}}{4}=144$

$\implies \dfrac{3a^{2}}{4}=144$

$\implies 3a^{2}=144\times4$

$\implies 3a^{2}=576$

$\implies a=576\div3$

$\implies a^{2}=192$

$\sf{Area\ of\ equilateral\ triangle =}\dfrac{\sqrt{3}}{\ 4}}\times a^{2}$

$\implies \dfrac{\sqrt{3}}{\ 4}}\times192$

$\implies \sqrt{3} \times 49$

$\implies 339.48$

∴ Area of the given equilateral triangle is $339.48cm^{2}$