Answer:
468 cm²
Explanation:
As with many composite shapes, there are many ways you can find the area. Here are three of them.
The area of any rectangle is the product of its length and width:
A = LW
The area of a trapezoid is ...
A = 1/2(b1 +b2)h
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1.
Subtract the area of the upper left corner rectangle from the overall outline rectangle.
overall - UL corner = (24 cm)(22 cm) - (5 cm)(12 cm) = 529 cm² -60 cm²
= 468 cm²
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2.
Draw a line from the left inside corner to the lower right corner. This divides the shape into two trapezoids. The bottom one has bases 5 cm and 24 cm, and height 10 cm. The upper one has bases 12 cm and 22 cm, and height 19 cm. The sum of their areas is ...
lower trapezoid + upper trapezoid = 1/2(5 +24)(10) +1/2(12 +22)(19)
= (29)(5) +(17)(19) = 145 +323 = 468 . . . cm²
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3.
Extend the vertical line on the left side so that it divides the figure into two rectangles the lower left one is 5 cm wide and 10 cm high. The larger right one is 19 cm wide and 22 cm high. The total area is ...
left rectangle + right rectangle = (5 cm)(10 cm) +(19 cm)(22 cm)
= 50 cm² +418 cm² = 468 cm²