9514 1404 393
Answer:
9350 m²
Step-by-step explanation:
There are several ways you can go at this. Here are 3 of them:
- along an extension of the lower right vertical edge, divide the figure into a rectangle and a right triangle.
- between the upper left corner and the inside corner at lower right draw a diagonal line to divide the figure into a trapezoid and a triangle.
- subtract the area of the trapezoid at the right from the area of the bounding rectangle
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The relevant formulas for area are ...
rectangle: A = LW . . . . . . . . . . . length times width
trapezoid: A = (1/2)(b1 +b2)h . . . b1, b2 are the bases, h is the height
triangle: A = (1/2)bh . . . . . . . . . . . b is the base, h is the height
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Here's what those computations look like:
1. rectangle: 60m wide by 80 m high = 4800 m².
right triangle: base 190-60 = 130 m; height = 80-10 = 70 m.
area = (1/2)(130 m)(70 m) = 4550 m²
figure area = 4800 m² +4550 m² = 9350 m² . . . . area of figure
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2. The trapezoid has bases of 80 m and 10 m, and a height of 60 m. Its area is ...
A = (1/2)(80 m +10 m)(60 m) = 2700 m²
The triangle has a base of 190 m and a height of 80-10 = 70 m. Its area is ...
A = (1/2)(190 m)(70 m) = 6650 m²
Then the total area is 2700 m² +6650 m² = 9350 m² . . . total area
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3. The bounding rectangle is 190 m by 80 m, so its area is ...
A = LW = (190 m)(80 m) = 15200 m²
The (negative) trapezoid at right has bases of 10 m and 80 m, and a width of 190-60 = 130 m. Its area is ...
A = (1/2)(10 m +80 m)(130 m) = 5850 m²
The area of the figure is the difference between these:
figure area = 15200 m² -5850 m² = 9350 m² . . . figure area
