Question

Derive formula for area of an isosceles triangle have equal side as a and base as b?​

Answer 1

Answer:

The area of an isosceles triangle is the amount of region enclosed by it in a two-dimensional space. The general formula for the area of triangle is equal to half the product of the base and height of the triangle. Here, a detailed explanation about the isosceles triangle area, its formula and derivation are given along with a few solved example questions to make it easier to have a deeper understanding of this concept.

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What is the Formula for Area of Isosceles Triangle?

The total area covered by an isosceles triangle is known as its area. For an isosceles triangle, the area can be easily calculated if the height (i.e. the altitude) and the base are known. Multiplying the height with the base and dividing it by 2, results in the area of the isosceles triangle.

What is an isosceles triangle?

An isosceles triangle is one which has at least two sides of equal length. This property is equivalent to two angles of the triangle being equal. An isosceles triangle has two equal sides and two equal angles. The name derives from the Greek iso (same) and Skelos (leg). An equilateral triangle is a special case of the isosceles triangle, where all the three sides and angles of the triangle are equal.

Isosceles Triangle

An isosceles triangle has two equal side lengths and two equal angles, the corners at which these sides meet the third side is symmetrical in shape. If a perpendicular line is drawn from the point of intersection of two equal sides to the base of the unequal side, then two right-angle triangles are generated.

Area of Isosceles Triangle Formula

The area of an isosceles triangle is given by the following formula:

Area = ½ × base × Height

Step-by-step explanation:

Answer 2

Step-by-step explanation:

The area of an isosceles triangle can be easily derived using Heron’s formula as explained below.

According to Heron’s formula,

Area = √[s(s−a)(s−b)(s−c)]

Where, s = ½(a + b + c)

Now, for an isosceles triangle,

s = ½(a + a + b)

⇒ s = ½(2a + b)

Or, s = a + (b/2)

Now,

Area = √[s(s−a)(s−b)(s−c)]

Or, Area = √[s (s−a)2 (s−b)]

⇒ Area = (s−a) × √[s (s−b)]

Substituing the value of “s”

⇒ Area = (a + b/2 − a) × √[(a + b/2) × ((a + b/2) − b)]

⇒ Area = b/2 × √[(a + b/2) × (a − b/2)]

Or, area of isosceles triangle = b/2 × √(a2 − b2/4)