Question

find the area of a triangle whose sides are 4.5 cm and 10 cm and perimeter 20.5 cm

Answer 1

Answer:

This question can be solved by using the Heron's Formula.

According to Heron's formula,

$\boxed{ \bf{Area = \sqrt{ s(s-a)(s-b)(s-c)}}}$

where,

's' is the semi perimeter, a,b,c are the sides of the triangle.

According to the question,

• p = 20.5 cm
• a = 4.5 cm
• b = 10 cm
• c = ?

We know that,

⇒ p = a + b + c

⇒ 20.5 = 4.5 + 10 + c

⇒ 20.5 = 14.5 + c

⇒ 20.5 - 14.5 = c

⇒ c = 6 cm

Calculating the semi perimeter we get:

⇒ s = p/2

⇒ s = 20.5/2

⇒ s = 10.25 cm

Substituting the values we get:

$\implies Area = \sqrt{ 10.25(10.25-4.5)(10.25-10)(10.25-6)}\\\\\\\implies Area = \sqrt{10.25 \times 5.75 \times 0.25 \times 4.25}\\\\\\\implies Area = \sqrt{ 62.62}\\\\\\\implies \boxed{ \bf{ Area \approx 7.91\:cm^2}}$