Question

what is the area of δabc if ad = 20, ab = 25, and cd = 9?

Explanation:

Step1: Find length of DB

In right triangle $\triangle ADB$, use Pythagorean theorem:
$$DB = \sqrt{AB^2 - AD^2}$$
$$DB = \sqrt{25^2 - 20^2} = \sqrt{625 - 400} = \sqrt{225} = 15$$

Step2: Calculate length of CB

Add lengths of CD and DB:
$$CB = CD + DB$$
$$CB = 9 + 15 = 24$$

Step3: Compute area of $\triangle ABC$

Use area formula for triangle: $\frac{1}{2} \times \text{base} \times \text{height}$
$$\text{Area} = \frac{1}{2} \times CB \times AD$$
$$\text{Area} = \frac{1}{2} \times 24 \times 20$$

Answer:

240