Answer:
- 288 cm²
- 61 ft²
Step-by-step explanation:
The dashed lines are included in the figure to help you see how it can be decomposed into shapes you know the area formulas for.
The relevant area formulas are ...
rectangle: A = LW . . . . . product of length and width
triangle: A = 1/2bh . . . . . half the product of base and height
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<h3>1.</h3>
There are three rectangles here:
left: A = (8 cm)(9 cm) = 72 cm²
top: A = (12 cm)(9 cm) = 108 cm²
lower right: A = (12 cm)(9 cm) = 108 cm²
The total area of these three rectangles is ...
(72 +108 +108) cm² = 288 cm²
The area of Figure 1 is 288 cm².
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<h3>2.</h3>
There is a rectangle here, along with a triangle.
rectangle: A = (10 ft)(4 ft) = 40 ft²
triangle: A = 1/2(6 ft)(3+4 ft) = 21 ft²
The total area of the parts of the figure is ...
(40 +21) ft² = 61 ft²
The area of Figure 2 is 61 ft².
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<em>Additional comment</em>
Figure 1 can be decomposed other ways:
- an overall 18×20 cm rectangle with a 9×8 cm rectangle removed from the upper left corner
- a 9×20 rectangle at the bottom with a 9×12 rectangle at the top
- a 9×8 rectangle at the left with an 18×12 rectangle at the right
Another way to decompose Figure 2 is as a trapezoid with a rectangle removed from the lower left. The trapezoid would have bases 10 and 10+6=16, and a height of 4+3=7. The removed rectangle is 10×3. (The computation we did is probably simpler.)
