Question

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Answer 1

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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 =

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

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

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

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

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

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

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

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

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.✮

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Answer 2

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

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Given = base (b) = 24cm.

perpendicular or height ( h) = 7cm.

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As we know area of Triangle =

$\frac{1}{2}$ × base × height

$\frac{1}{2} \times 24 \times 7$

$= \frac{1}{2} \times 168$

$= 84 {cm}^{2}$

∴ area=$\bold{\huge{\fbox{\color{maroon}{84cm²}}}}$

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