Chapter 12: Heron’s Formula

(A) √32 cm

Explanation:

Let height of triangle = h

As the triangle is isosceles,

Let base = height = h

According to the question,

Area of triangle = 8cm²

⇒ ½ × Base × Height = 8

⇒ ½ × h × h = 8

⇒ h² = 16

⇒ h = 4cm

Base = Height = 4cm

Since the triangle is right angled,

Hypotenuse² = Base² + Height²

⇒ Hypotenuse² = 4² + 4²

⇒ Hypotenuse² = 32

⇒ Hypotenuse = √32

Hence, Options A is the correct answer.

(D) 100√3 m²

Explanation:

Area of an equilateral triangle of side a = √3/4 a²

According to the question,

Perimeter of triangle = 60m

⇒ a + a + a = 60

⇒ 3a = 60

⇒ a = 20m

Area of the triangle = (√3/4) a²

= (√3/4) (20)²

= (√3/4) (400)

= 100√3

Hence, Options D is the correct answer.

(C) 1344 cm²

Explanation:

According to the question,

Sides of a triangle,

a = 56, b = 60, c = 52

s = (a + b + c)/2

⇒ s = (56 + 60 + 52)/2

= 168/2 = 84.

Area of triangle = √s(s-a)(s-b)(s-c)

= √84(84-56)(84-60)(84-52)

= √84×28×24×32

= 1344cm²

Hence, Options C is the correct answer.

(A) 5.196 cm²

Explanation:

Area of an equilateral triangle of side a = √3/4 a²

According to the question,

a = 2√3

Area of triangle = (√3/4) a²

= (√3/4) (2√3)²

= (√3/4)(12)

= 3√3

= 5.196

Hence, Options A is the correct answer.