Question

of the triangle.
The base of an isosceles triangle is 12 cm and its perimeter is 32 cm. Find its area.​

Answer 1

Side a = 12 cm

Side b = 12 cm (Two sides are equal in an isoceles triangle)

Side c = ?

Perimeter = 32 cm

Area = ?

Side c = Perimeter - (side a + side b)

= 32 - (12+12)

= 32 - 24

= 8

therefore side c = 8 cm

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

= 1/2 × 24 × 8

= 96

Therefore, area of triangle = 96 cm

Hope it helps :)

Answer 2

Area Of Triangle = 48 cm²

Step-by-step explanation:

GIVEN

Base = 12 cm

Perimeter = 32 cm

___________________________

TO FIND

Area Of Triangle

___________________________

We know that,

Perimeter Of Triangle = a + b + c

We know that,

Given triangle is isosceles triangle

Therefore,

Perimeter Of Triangle = a + a + b

32 = 2a + 12

2a = 32 - 12

2a = 20

a = 20 / 2

a = 10

a = 10 cm

___________________________

Now,

Let's find area of triangle

We know that,

Area Of Triangle = ½ × Base × Height

To find area of triangle we have to find the height

To find the height

Let's divided the triangle in 2 equal parts

We know that,

Hypotenuse² = Base² + Height²

Here,

We have

Hypotenuse = 10 cm

Base = 12 / 2 = 6 cm

Height = ?

We know that,

Hypotenuse² = Base² + Height²

Height² = Hypotenuse² - Base²

Height² = 10² - 6²

Height² = 100 - 36

Height² = √64

Height = 8

Height = 8 cm

___________________________

Now,

Let's find area of triangle

We know that,

Area Of Triangle = ½ × Base × Height

Area Of Triangle = ½ × 12 × 8

Area Of Triangle = ½ × 96

Area Of Triangle = 48

Area Of Triangle = 48 cm²