Question

find the area of the right triangle.
be sure to include the correct unit in your answer.
area:

Explanation:

Step1: Apply Pythagoras theorem to find the other leg

In a right - triangle, by Pythagoras theorem \(a^{2}+b^{2}=c^{2}\). Let the legs be \(a = 20\) and \(b\), and hypotenuse \(c = 29\). Then \(b^{2}=c^{2}-a^{2}\).

$$b^{2}=29^{2}-20^{2}=841 - 400=441$$

$$b=\sqrt{441}=21$$

Step2: Use the area formula for a right - triangle

The area formula for a right - triangle is \(A=\frac{1}{2}\times\text{base}\times\text{height}\). Here, base \(a = 20\) and height \(b = 21\)

$$A=\frac{1}{2}\times20\times21$$

$$A = 10\times21$$

Answer:

\(210\space m^{2}\)