Answer:
90.0 cm²
Explanation:
You want to know the area of the composite figure shown.
Dimensions
The vertical side and hypotenuse of the right triangle are 9 cm and 15 cm. These have the ratio 9/15 = 3/5, so we know this triangle is a 3-4-5 right triangle with a scale factor of 3. The missing side length is 3·(4 cm) = 12 cm.
Area
So, the figure is a trapezoid with a top base of 4 cm, a bottom base of 4+12 = 16 cm, and a height of 9 cm. Its area is ...
A = 1/2(b1 +b2)h
A = 1/2(4 cm +16 cm)(9 cm)
A = 90 cm²
The area of the figure is 90.0 cm².
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Additional comment
In case you don't recognize the 3:4:5 side ratio, you can figure the base of the triangle using the Pythagorean theorem:
a² +b² = c²
a² = c² -b² = 15² -9² = 225 -81 = 144
a = √144 = 12 . . . . . length of CD in cm
Other useful Pythagorean triples you will see are {5, 12, 13}, {7, 24, 25}, {8, 15, 17}.