Question

find the are of the isosceles triangle has perimeter 30 cm and each equal side is 8 cm find area of the triangle​

Answer 1

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GiveN:

• Perimeter of the triangle = 30 cm
• Each equal side = 8 cm

To FinD:

• Area of the isoceles triangle?

Step-wise-Step Explanation:

Two sides are equal in an isoceles triangle. Hence, teh Perimeter will be:

➛ 2(Equal side) + Unequal side = 30 cm

➛ 2(8 cm) + Unequal side = 30 cm

➛ 16 cm + Unequal side = 30 cm

➛ Unequal side = 14 cm

Hence the sides of the triangle are 8 cm, 8 cm and 14 cm. We can use Heron's formula for finding the area of ∆.

$\boxed{\rm{Ar. \: of \: \triangle = \sqrt{s(s - a)(s - b)(s - c)} }}$

Semiperimeter = 30 cm / 2 = 15 cm

Putting the given values:

➛ $\sf{Ar. \: of \: \triangle = \sqrt{15(15 - 8)(15 - 8)(15 - 14)} }$

➛ $\sf{Ar. \: of \: \triangle = \sqrt{15 \times 7 \times 7 \times 1 \: }{cm}^{2} }$

➛ $\sf{Ar. \: of \: \triangle = 7 \sqrt{15} \: {cm}^{2} }$

➛ $\sf{Ar. \: of \: \triangle \approx \: 27.11 \: {cm}^{2} }$

Hence,

• The required area of the isoceles triangle is approximately 27. 11 cm²

Answer 2

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An isosceles triangle has perimeter 30cm and each of the equal sides is 12cm. Find the area of the triangle.

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Perimeter of isosceles triangle=30cm

Length of equal sides=12cm

Let third side of triangle=xcm

According to problem,

x+12+12=30

x+24=30

x=30−24

x=6

∴ Third side of triangle=6cm

Using Heron's formula,

Area of triangle= √s(s−a)(s−b)(s-c) sq. units

where s=

a+b+c/2

s=30/2=15

Area of triangle=

√15(15−12)(15−12)(15−6) cm²

=3×3×√15cm²

=9√15cm²

therefore,area of triangle=9√15cm²

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