Geometry

Question Analysis

The main focus is on calculating the area of the given triangle. First, we need to determine the base length using the Pythagorean theorem, and then apply the formula for the area of a triangle .

 

Key Concept Explanation

The area  of a triangle is calculated with the formula , where  is the base and  is the height. The Pythagorean theorem  (where  is the hypotenuse and ,  are the other two sides) helps us find the missing side length when the hypotenuse and one side are known.

 

Step - by - Step Solution

1. Find the base length:

Consider the right - angled triangle formed. The hypotenuse is  and the height is . Let the base of this right - angled triangle be . According to the Pythagorean theorem, .

But the base of the large triangle .

2. Calculate the area:

The height

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