Question

find the total surface area of the figure. 15

Explanation:

Step1: Calculate area of right triangle

First, find the base of the right triangle using the Pythagorean theorem:
Let the base be $b$, so $b = \sqrt{17^2 - 8^2} = \sqrt{289 - 64} = \sqrt{225} = 15$.
Area of triangle: $\frac{1}{2} \times 8 \times 15 = 60$

Step2: Calculate area of parallelogram

The base of the parallelogram is 15, height is 18.
Area of parallelogram: $15 \times 18 = 270$

Step3: Sum all surface areas

Add the area of the triangle, parallelogram, and the shared side is internal so not counted. Total area is sum of the two shapes.
Total area: $60 + 270 = 330$

Answer:

330