Question

Find the area of a triangle if it's sides are 21cm, 17cm, 10cm ​

Answer 1

Answer:

perimeter of the triangle (21+17+10) cm

=48cm

half of the perimeter=48/2cm=24 cm

so, area

=√(24)(24-21)(24-17)(24-10) sq cm

=√(24×3×7×14 sq cm

=√(3×2×2×2×3×7×2×7) sq cm

=3×2×2×7 sq cm

=84 sq cm

Answer 2

✴Question:-

Find the area of a triangle if it's sides are 21cm, 17cm, 10cm

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✴Solution:-

→Given:-

• a=10cm
• b=21cm
• c=17cm

→To Find:-

• Area of Triangle.

→Concept:-

• Simple Area/Perimeter Problem.

→Formula:-

• $Area = \sqrt{S(s−a)(s−b)(s−c) }$

→Calculation:-

We Know,

$S= \frac{a + b + c}{2}$

$⇒S=\frac{21cm+17cm+10cm}{2}$

$⇒S=\frac{48cm}{2}$

$⇒S=24cm$

So,

$Area = \sqrt{S(s−a)(s−b)(s−c) }$

$⇒Area= \sqrt{24cm(24−21cm)(24−17cm)cm(24−10)cm}$

$⇒Area=\sqrt{24cm×3cm×7cm×14cm}$

$⇒ Area=\sqrt{{72cm}^{2} × {98cm}^{2}}$

$⇒Area={84cm}^{2}$

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✴Final Answer:-

∴ Area of the triangle with sides 21cm, 17cm and 10cm is ${84cm}^{2}$

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✴Note:-

For finding out the area of a scalene triangle, we need to do the following measurements:-

a).The length of one side of the triangle and the perpendicular distance of that particular side to the opposite angle.

b).The lengths of all three sides of the triangle.

So, Area of scalene triangle is given by: - and here,$S= \frac{a + b + c}{2}$where a, b, c are sides of triangle and 'S' is the semi-perimeter of triangle having sides a,b,c.

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