Question

An isosceles triangle
equal side is 12cm.
has perimeter 3om
Find the area of the triangle.​

Answer 1

Answer:

Step-by-step explanation:

Area of triangle=√s(s-a)(s-b)(s-c),

Here,s is semi-perimeter,

And,a,b,c are the sides of the triangle.

Given,triangle is isosceles:

In Isosceles triangle two sides are equal,

So a =b=12 cm,

and Perimeter is 30 cm,

Semi-Perimeter=s=Perimeter/2,

s=30/2,

s=15 cm.

We need to find c which is base,

Perimeter=30 cm,

a+b+c=30,

12+12+c=30,

24+c=30,

c=30-24,

c=6.

Area of triangle is √s(s-a)(s-b)(s-c),

Putting a =12,b=12c=6 and s=15.

√15(15-12)(15-12)(15-6),

√15(3)(3)(9),

√15(9)(9),

√9*9*√15,

√9^2*√15,

(9)*√15,

9√15,

Thus area is 9√15 cm^2.

Hope it helps you.

Answer 2

Answer:

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=2a+b+c

s=230=15

Area of triangle=15(15−12)(15−12)(15−6)cm2

=15×3×3×9cm2

=3×3×15cm2

=915cm2

∴ Area of triangle=915cm2.