The base of an isosceles triangle is 10 cm and one of its equal sides is 13 cm. Find its area using Heron’s formula.

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60 cm2

80 cm2

50 cm2

90 cm2

answer is A.

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Detailed Solution

Concept- We'll calculate the triangle's semi-perimeter as well as the distance between each side and the semi-perimeter. These values will be used as replacements in Heron's formula. After that, we'll figure out the area and solve the phrase.
formulas employed
The following formulas will be applied:
1) A triangle's semi-perimeter is equal to half of the sum of its side lengths:

s = \frac{a + b + c}{2}

2) The area of a triangle with sides a, b, and c and a semi-perimeter s is given by the Heron's formula:

A = \sqrt s (s - a) (s - b) (s - c) .

We are aware that an isosceles triangle has two equal sides. Given that one of the equal sides is 13 cm long, the other equal side must also be 13 cm long.
We will start by determining the triangle's semiperimeter. In the semi-perimeter formula, we will change a and b and c to 10 and 13, respectively. As a result, we have

s = \frac{10 + 13 + 13}{2}

s = \frac{36}{2}

s = 18 .

We shall now calculate the value of s-a. When we substitute 10 for a and 18 for s, the result is 18-10=8.
-We'll determine the value of s-b. We obtain 18-13=5 by substituting 13 for b and 18 for s.
We'll determine the value of s-c. 13 for c and 18 for s in the formula
we obtain ⇒18−13=5
We shall now calculate the triangle's area.—The Heron's formula,