Geometry

Question Analysis

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

 

Key Concept Explanation

1. Pythagorean theorem: For a right - angled triangle, , where  is the hypotenuse and ,  are the other two sides. It helps us find the unknown side length.

2. Area of a triangle: The area  of a triangle is calculated by the formula , where  is the base and  is the height.

 

Step - by - Step Solution

1. Find the length of the base plus the extended line:

Using the Pythagorean theorem, for the right - angled triangle with hypotenuse  and height , let the base of this right - angled triangle (base plus extended line) be . Then .

2. Find the actual base of the triangle:

Given the extended line length is , the actual base