Area of the triangle whose sides are 13 cm - 9 cm and 6 cm isA- 23-6 m 2B- 26-3 m 2- 36-34 m 2D- 23-66 m 2

The correct option is D 23.66 m^2 The sides of the triangle are a = 13cm, b = 9cm and c = 6cm s =a+b+c/2=13+9+6/2=14 cm ∴ Area of the triangle =√(s(s a)(s b)( ...

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Standard VIII

Mathematics

Area of Special Triangles

Area of the t...

Question

Area of the triangle whose sides are 13cm, 9cm and 6cm is

$23.6 m^{2}$

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$26.3 m^{2}$

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$36.34 m^{2}$

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$23.66 m^{2}$

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Solution

The correct option is D
$23.66 m^{2}$

The sides of the triangle are a = 13cm, b = 9cm and c = 6cm
$s = \frac{a + b + c}{2} = \frac{13 + 9 + 6}{2} = 14 c m$
$∴$ Area of the triangle
$= \sqrt{s (s - a) (s - b) (s - c)}$ [Heron’s formula]
$= \sqrt{14 (14 - 13) (14 - 9) (14 - 6)} c m^{2}$
$= \sqrt{14 \times 1 \times 5 \times 8} c m^{2} = \sqrt{560} c m^{2}$
$= 23.66 c m^{2}$

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Area of the triangle whose sides are 13cm, 9cm and 6cm is

The correct option is D 23.66 m2 The sides of the triangle are a = 13cm, b = 9cm and c = 6cm s=a+b+c2=13+9+62=14 cm ∴ Area of the triangle =√s(s−a)(s−b)(s−c) [Heron’s formula] =√14(14−13)(14−9)(14−6) cm2 =√14×1×5×8 cm2=√560 cm2 =23.66 cm2