Geometry

Question Analysis

The main focus is on calculating the area of the given triangle. Since the height isn't directly given, we need to use the Pythagorean theorem to find it first, and then apply the triangle - area formula.

 

Key Concept Explanation

The area  of a triangle is calculated by 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 unknown side (height in this case).

 

Step - by - Step Solution

1. Find the height:

First, consider the right - angled triangle formed. The hypotenuse is , and the base of this right - angled triangle (the side along the base of the large triangle) is .

According to the Pythagorean theorem, .

2. Calculate the area:

The base of the large triangle

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