Question

18. Find the area of an equilateral triangle of side 2√2​

Answer 1

GIVEN :-

• Side of equilateral triangle = 2√2 units.

TO FIND :-

• The area of an equilateral triangle.

SOLUTION :-

As we know that,

$\\ : \implies \displaystyle \sf \: Area \: of \: Equilateral \: \triangle = \frac{ \sqrt{3} }{4} \times (side) ^{2}$

$: \implies \displaystyle \sf \: Area \: of \: Equilateral \: \triangle = \frac{ \sqrt{3} }{4} \times (2 \sqrt{2} ) ^{2}$

$: \implies \displaystyle \sf \: Area \: of \: Equilateral \: \triangle = \frac{ \sqrt{3} }{4} \times (2 \times 2 \times \sqrt{2} \times \sqrt{2} )$

$: \implies \displaystyle \sf \: Area \: of \: Equilateral \: \triangle = \frac{ \sqrt{3} }{4} \times (4 \sqrt{4} )$

$: \implies \displaystyle \sf \: Area \: of \: Equilateral \: \triangle = \frac{ \sqrt{3} }{4} \times (4 \times 2)$

$: \implies \displaystyle \sf \: Area \: of \: Equilateral \: \triangle = \frac{ \sqrt{3} }{4} \times 8$

$: \implies \displaystyle \sf \: Area \: of \: Equilateral \: \triangle = 2 \sqrt{3}$

$: \implies \underline{ \boxed{ \displaystyle \sf \: Area \: of \: Equilateral \: \triangle = 3.46 \: unit ^{2} }}$

$\therefore\underline{\textsf{ Area of equilateral triangle is 3.46 .}}$

Answer 2

$\underline{\underline{\purple{\sf Given:}}}$

• Side of the Triangle = 2√2 units

$\underline{\underline{\purple{\sf Find:}}}$

• Area of Triangle

$\underline{\underline{\purple{\sf Solution:}}}$

we, know that

$\underline{\boxed{ \sf Area \: of \: equilateral \triangle = \dfrac{\sqrt{3} }{4} \times {(side)}^{2}}}$

where,

• Side = 2√2 units

So,

$\sf \to Area \: of \: equilateral \triangle = \dfrac{\sqrt{3} }{4} \times {(side)}^{2}$

$\sf \to Area \: of \: equilateral \triangle = \dfrac{\sqrt{3} }{4} \times {(2 \sqrt{2} )}^{2}$

$\sf \to Area \: of \: equilateral \triangle = \dfrac{\sqrt{3} }{4} \times (4 \times 2)$

$\sf \to Area \: of \: equilateral \triangle = \dfrac{\sqrt{3} }{ \not{4}} \times \not{8}$

$\sf \to Area \: of \: equilateral \triangle = \sqrt{3} \times 2$

$\sf \to Area \: of \: equilateral \triangle = 2 \sqrt{3} \: {units}^{2}$

$\rule{300}{3}$

Hence, the area of Triangle will be 2√3 units²