Question

each side of an equilateral measure find the area of the triangle in 10 cm find the area

Answer 1

since , side = 10cm = a

and , the triangle is equilateral.

we know that ,

area of an Equilateral triangle ,

= $\frac{\sqrt{3}}{4} {a}^{2}$

substitute the value of "a" which is the side of the triangle.

= $\frac{\sqrt{3}}{4} {(10)}^{2}$

= $\frac{\sqrt{3}}{4}$ × 10 × 10

= $\frac{\sqrt{3}}{\cancel{4}}$ × $\cancel{100}$

divide 100 by 4 , so 100 ÷ 4 = 25.

= $\sqrt{3}$ × 25

$= \bf\huge25 \sqrt{3} \: {cm}^{2}$

Thus , area of the equilateral triangle $= \bf25 \sqrt{3} \: {cm}^{2}$

Answer 2

Here's the answer

$\bf {Given => }$

Side of an equilateral triangle = 10 cm.

$\bf {To \: find => }$

Area of the triangle = ?

$\bf {Solution => }$

We know that,

$\sf{Area \: of \: equilateral \: triangle = }\\ \sf{ \frac{ \sqrt{3} }{4} \times {side}^{2} }$

As Given ,

$\sf{ = \frac{ \sqrt{3} }{4} \times (1 0 {)}^{2}}$

$\sf{ = \frac{ \sqrt{3} }{4} \times 10 \times 10}$

$\sf{ = \frac{ \sqrt{3} }{4} \times 100}$

Simplify it, we get

$\sf{ = \sqrt{3} \times 25}$

$\sf{ = 25\sqrt{3}} \: cm {}^{2}$

Thus
The area of the triangle is 25 √3 sq. cm

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Thanks!!