Question

find the area of a right angled triangle if it's base is 24 centimetre and perpendicular 7 centimetres​

Answer 1

Given :-

Base of the Triangle = 24 cm

Perpendicular = 7 cm

Have to find :-

Area of the Triangle = ?

Diagram :-

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\linethickness{.4mm}\put(1,1){\line(1,0){4.5}}\put(1,1){\line(0,1){3.5}}\qbezier(1,4.5)(1,4.5)(5.5,1)\put(-1,2.5){\large\bf 7\ cm}\put(2.4,.3){\large\bf 24\ cm}\put(1.02,1.02){\framebox(0.3,0.3)}\end{picture}$

Solution :-

Method - 1

As it is a right angle triangle

So,

The area of Triangle = ½ × Base × Height

As from given :-

Base ↬ 24

Height = Perpendicular ↬ 7

Putting up the values in the above formula :-

$\longmapsto\tt{A=\dfrac{1}{{\cancel{2}}}\times{7}\times{{\cancel{24}}}}$

$\longmapsto\tt{A=7\times{12}}$

$\longmapsto\tt\bf{84\:{cm}^{2}}$

_______________________

Method - 2

Let's find out the hypotenese .

We know the Pythagoras Theorem

(Hypotense)² = (Perpendicular)² + (Base)²

(Hypotense)² = (7)² + (24)²

(Hypotense)² = 49 + 576

(Hypotense)² = 625

(Hypotense) = √625

(Hypotense) = 25 cm.

We got

➤ a = 24 cm

➤ b = 7 cm

➤ c = 25 cm

Now,

Applying the Heron's Formula

$\bold{According \: to \: heron's \: formula} \\ \tt: \implies s = \frac{a + b + c}{2} \\ \\ \tt: \implies s = \frac{24+ 7+ 25}{2} \\ \\ \tt: \implies s = \frac{56}{2} \\ \\ \bf{\tt: \implies s =28} \\ \\ \bold{For \: Area \: of \: triangle} \\ \tt: \implies Area \: of \: triangle = \sqrt{s(s - a)(s - b)(s - c)} \\ \\ \tt: \implies Area \: of \: triangle = \sqrt{28(28- 25)(28 - 7)(28 - 24)} \\ \\ \tt: \implies Area \: of \: triangle = \sqrt{28 \times 3 \times 21\times 4 } \\ \\ \tt: \implies Area \: of \: triangle = \sqrt{1056} \\ \\ \bf{\tt: \implies Area \: of \: triangle = 84 \: {cm}^{2} }$

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Answer 2

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Find the area of a right angled triangle if it's base is 24 cm and perpendicular 7 cm.

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➡Area of triangle is 84cm²

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• Perpendicular of triangle = 7cm
• Base of triangle = 24cm

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• Area of Triangle

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Pythagorous Theorem =

$\bf \orange{ {Hypotenuse}^{2} = {Base}^{2} + {Perpendicular}^{2} }$

Heron's Formula =

$\bf \pink{ \sqrt{s(s - a)(s - b)(s - c)} }$

$\bf {\underline {\underline{✤ SƠԼƲƬƖƠƝ}}}$

In this question, first we will find Third side using Pythagorous Theorem then area of Triangle by Heron's Formula.

$\sf \purple{Let's \: start }$

$\bf { {Hypotenuse}^{2} = {Base}^{2} + {Perpendicular}^{2} }$

$\bf {\large\to} {Hypotenuse}^{2} = {24}^{2} + {7}^{2}$

$\bf {\large\to} {Hypotenuse}^{2} = 567 + 49$

$\bf {\large\to} {Hypotenuse}^{2} = 625$

$\bf {\large\to} {Hypotenuse} = \sqrt{625}$

$\bf {\large\to} {Hypotenuse} = 25cm$

Area of Triangle,

Let

a = 24cm

b = 7cm

c = 25cm

Semi perimeter (s)

= 24 + 7 + 25/ 2

= 56/2

= 28cm

$\bf { \sqrt{s(s - a)(s - b)(s - c)} }$

$\bf \sqrt{28(28 - 24)(28 - 7)(28 - 25)}$

$\bf \sqrt{28 \times 4 \times 21 \times 3}$

$\bf \sqrt{7056}$

$\bf 84 {cm}^{2}$

Therefore, Area of triangle is 84cm².

$\bf \pink{hope \: } \purple{it \: } \blue{helps \: } \red{uh..}$