Chapter 12: Heron’s Formula

False

Justification:

Area of triangle = ½ × Base × Altitude

= ½ × 4 × 6

= 12cm²

Hence, the statement “the area of a triangle with base 4 cm and height 6 cm is 24 cm²” is False.

True

Justification:

Area of triangle = ½ × Base × Altitude

= ½ × 4 × 4

= 8cm²

Hence, the statement is “area of △ABC is 8 cm² in which AB = AC = 4 cm and ∠A = 90º” is True.

True

Justification:

According to the question,

Perimeter = 11cm

And base, a = 5

As the triangle is isosceles, b = c

Perimeter = 11

⇒ a + b + c = 11

⇒ 5 + b + b = 11

⇒ 5 + 2b = 11

⇒ 2b = 6

⇒ b = 3

So, we have,

a = 5, b = 3, c = 3

s = (a + b + c)/2

⇒ s = (5 + 3 + 3)/2 = 11/2

Area of triangle = √s(s-a)(s-b)(s-c)

⇒ Area of triangle = (5√11)/4cm²

Hence, the statement “The area of the isosceles triangle is 5/4 √11cm², if the perimeter is 11 cm and the base is 5 cm” is True.

False

Justification:

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

According to the question,

Area of a triangle = 20√3 cm²

⇒ √3/4 a² = 20√3

⇒ a² = 20× 4

⇒ a² = 80

⇒ a = 4√5 cm

Hence, the statement “the area of the equilateral triangle is 20√3 cm² whose each side is 8 cm” is False.