Question

if the base of an isosceles triangle is 12 cm and it's perimeter is 35 cm , find the area of the triangle​

Answer 1

Required Answer :

The area of the isosceles triangle = 58.86 cm²

Given :

• Base of an isosceles triangle = 12 cm
• Perimeter of the triangle = 35 cm

To find :

• Area of the triangle

Solution :

Here, in this question we are provided the base and perimeter of an isosceles triangle and we need to calculate the area of triangle. So, firstly we will calculate the two equal sides of the triangle by using the formula of perimeter of isosceles triangle and then by using the formula of area of isosceles triangle we will calculate its value.

Calculating the other sides of the triangle :

Using formula,

• Perimeter = a + a + b

where,

• a denotes the two equal sides of the triangle
• b denotes the third side

In isosceles triangle 2 sides are equal to each other.

Substituting the given values :

→ 35 = a + a + 12

→ 35 - 12 = 2a

→ 23 = 2a

→ 23/2 = a

→ 11.5 = a

Therefore, the two equal sides of the triangle = 11.5 cm

Using formula,

• Semi - Perimeter = Perimeter ÷ 2

Substituting the given values :

→ Semi perimeter = 35 ÷ 2

→ Semi perimeter = 17.5 cm

Using formula,

• Heron's formula = √s(s - a)(s - b)(s - c)

Substituting the given values :

→ Area = √(17.5(17.5 - 11.5)(17.5 - 11.5)(17.5 - 12)

→ Area = √17.5(6)(6)(5.5)

→ Area = √3465

→ Area = 58.86

Therefore, the area of the isosceles triangle = 58.86 cm²

Answer 2

Step-by-step explanation:

ANSWER ✍️

_______________

Let the sides be x, x, 12 then 35=2x+12

• ⇒x=11.5cm
• AD= √(11.5) ^2-6^2=9.81cm

Area of ABC= 1/2 (BC)(AD)

• = 1/2(12)(9.81)
• =58.86cm

hope this helps you ☺️