Question

The base of an isosceles triangle is 12 cm and its
perimeter is 32 cm. Then its area is

Answer 1

Answer:

$48 {cm}^{2}$

Given:

Base of isosceles triangle=12 cm

Perimeter=32 cm

To find:Area

Construction:Draw A perpendicular at BC taking as H

Solution:-

base=12cm and perimeter=32cm

Let other two sides be a

We know that

perimeter of isosceles triangle=Sum of all sides

a+b+a=32

2a+12=32

2a=32-12

2a=20

a=10

Finding h

${h}^{2} +{b}^{2} = {p}^{2}$

${h}^{2} +{6}^{2} = {10}^{2}$

${h}^{2} + 36 = 100$

${h}^{2} = 64$

$h = \sqrt{64}$

$h = 8 \: cm$

we have base=12cm and height=8cm

Now Area of triangle=1/2×b×h

$\frac{1}{2}\times 12\times8$

$48 \: {cm}^{2}$

------------

Therefore Its area=48 cm^2

Answer 2

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Given:-

The base of an isosceles triangle = 12cm

Perimeter = 32cm

To find :-

The area of the isosceles triangle

Solution:-

Let the measures of three sides of the triangle be, x cm, 12cm & x cm, respectively.

Perimeter of an isosceles triangle = x + 12 + x = 32

2x + 12 = 32

2 x = 32 -12

2x = 20

x = $\bf\large\frac{20}{2}$

x = 10 cm.

We have the side of the triangle, we need to calculate the height of the triangle,

h² + b² = x²

h² + 6² = 10²

h² + 36 = 100

h² = 100 -36

h² = 64

h=√64

h = 8cm

Area of the triangle = 1/2 × base × height

Area of triangle = 1/2 × 12 × 8

Area of the triangle = 6 × 8

Area of the triangle = 48cm²