Question

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

Answer 1

Answer:-

★ Given:-

• An isosceles triangle of two equal sides

1. First side = 12cm
2. Second side = 12cm

• Perimeter of triangle = 30 cm

★ To Find:-

• Area of the given triangle

★ Solution:-

➫ Finding the length of third Side:

According to the given conditions;

Perimeter of triangle = 30 cm

➟ Sum of all sides = 30cm

➟ First side + second side + third side = 30cm

➟ 12cm + 12cm + third side = 30cm

➟ 24 cm + third side = 30cm

➟ third side = 30 - 24

∴ Third Side = 6cm

➫ Finding the value of s

Here,

s = Semi- Perimeter

Semi- Perimeter

= Perimeter ÷ 2

= 30 ÷ 2

= 15 cm

∴ Value of s is 15 cm

➫ Finding the area of triangle

Area of triangle by Heron's Formula

√s (s-a) (s-b) (s-c)

Here,

• s = semi - perimeter = 15cm
• a = first side = 12cm
• b = second side = 12cm
• c = third side = 6cm

By putting the values;

Area of triangle

= √15 (15-12) (15-12) (15-6)

= √3 × 5 × 3 × 3 × 3 × 3

= 3 × 3 √15

= 9√15 cm²

∴ Area of triangle is 9√15 cm²

★ Formula to be remembered:-

• Area of square = Side × Side

• Area of rectangle = length × breadth

• Area of rhombus = ½ × d¹ × d²

• Area of parallelogram = Base × Height

• Area of triangle = ½ × Base × Height

or by Heron's Formula

Answer 2

Given :

An is isosceles triangle has perimeter 30cm and  each of its equal sides is 12 cm.

To find :

Find the area of  the triangle.

Solution :

Let the unequal side be 'b' cm

Each equal side, a = 12 cm.

Perimeter = Sum of all 3 sides

⇒ 30 = 12 + 12 + b

⇒ 30 = 24 + b

⇒ b = 30 - 24

⇒ b = 6 cm.

Now using formula :

Area of isosceles triangle = b/4 [√(4a² - b²)]

Now putting values,

⇒ Area of Δ = 6/4 × [√(4 × 12² - 6²)]

⇒ Area of Δ = 3/2 × [√(4 × 144 - 36)]

⇒ Area of Δ = 3/2 × [√(576 - 36)]

⇒ Area of Δ = 3/2 × [√540]

⇒ Area of Δ = 3/2 × 23.238

⇒ Area of Δ = 34.857 cm²

∴ Area of isosceles triangle = 34.857 cm²