Question

4. The base of an isosceles triangle is 8 cm long and each of its equal sides
measures 6 cm. The area of the triangle is
(a) 16√5 cm² (b) 8√5 cm²
(c) 16/3 cm²
(d) 8√3cm²....​

Answer 1

Answer:

(b) 8√5 cm² ✔

Explanation:

Given

• Base of isosceles triangle = 8cm
• Measure of each equal side = 6cm

To Find

• Area of the triangle

Solution

We are given with all three sides of the triangle, So we can find the area of the triangle by Heron's formula.

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

• s = 1/2 × perimeter
• a,b and c are the sides of the triangle.

Finding semi-perimeter ( s )

s = 1/2 × ( 8cm + 6cm + 6cm )

s = 1/2 × 20cm

s = 10cm

Substitute value of s in the formula.

⟹ √{ s (s - a )(s - b)(s - c) }

⟹ √{10 ( 10 - 8 )(10 - 6)(10 - 6)}

⟹ √(10 × 2 × 4 × 4 )

⟹ √( 2 × 5 × 2 × 4 × 4)

⟹ √( 2² × 4² × 5 )

⟹ 2 × 4 √5

⟹ 8√5

8√5 cm² is the area of the triangle.