Question

7. In a A ABC, AB = AC = 4 cm and ZA = 90°. Calculate the area of triangle ABC. a Find the area of the equilateral triangle whose each side is : (i) 12 cm, (ii) 5 cm. = = = 8​

Answer 1

$\huge\underline{\underline{\mathfrak\red{Given::}}}$

$\large\mathtt\blue{Question\:1:}$

$\small\text{In a A ABC, AB = AC = 4 cm and ZA = 90°. } \\ \small\text{Calculate the area of triangle ABC.}$

$\large\mathtt\blue{Question\:2:}$

$\small\text{Find the area of the equilateral triangle } \\\small\text{whose each side is : (i) 12 cm, (ii) 5 cm}$

$\huge\underline{\underline{\mathfrak\red{Solution::}}}$

$\large\mathtt\blue{Answer\:1:}$

$\bf{AC = AB =\red {4 \: cm} \: and \: angle \: A=\red 9\red0°} \\ \\ \bf{Area \: of \: a \: triangle \: ABC= \red{ \frac{1}{2} ×base×height}} \\ \\ \bf{Area \: of \: a \: triangle \: ABC= \red{ \frac{1}{2} ×AB×AC}} \\ \\ \bf{Area \: of \: a \: triangle \: ABC= \red{ \frac{1}{2} ×4×4}} \\ \\ \bf{Area \: of \: a \: triangle \: ABC= \red{ \frac{1}{\cancel2} ×\cancel4×4}} \\ \\ \bf{Area \: of \: a \: triangle \: ABC= \boxed{\mathfrak\pink{ 80 {cm}^{2} }}}$

$\large\mathtt\blue{Answer\:2:}$

$\bf{i) \: Side=\red{12 \: cm}} \\ \\ \bf{ Area \: of \: equilateral \: triangle =\red{ \frac{ \sqrt{3} }{4 } \times {side}^{2} }} \\ \\ \bf{Area \: of \: equilateral \: triangle =\red{ \frac{ \sqrt{3} }{4 } \times {12}^{2} }} \\ \\ \bf{Area \: of \: equilateral \: triangle =\red{ \frac{ \sqrt{3} }{4 } \times 144 }} \\ \\ \bf{Area \: of \: equilateral \: triangle = \boxed{\mathfrak\pink{ 36\sqrt{3} \: {cm}^{2} }}}$

$\\ \\ \bf{ii) \: Side=\red{5 \: cm}} \\ \\ \bf{ Area \: of \: equilateral \: triangle =\red{ \frac{ \sqrt{3} }{4 } \times {side}^{2} }} \\ \\ \bf{Area \: of \: equilateral \: triangle =\red{ \frac{ \sqrt{3} }{4 } \times {5}^{2} }} \\ \\ \bf{Area \: of \: equilateral \: triangle =\red{ \frac{ \sqrt{3} }{4 } \times 25 }} \\ \\ \bf{Area \: of \: equilateral \: triangle = \boxed{\mathfrak\pink{ \frac{25 \sqrt{3} }{4} \: {cm}^{2} }}}$

$\\ \\ \boxed{\mathfrak\green{ hope \: it \: help }}$