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I’m trying to find the area by using b1+b2xh divided by 2

I’m trying to find the area by using b1+b2xh divided by 2-example-1
User SnowFrog
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1 Answer

3 votes

Answer:

300 ft²

Explanation:

You want the area of the symmetrical 5-sided figure shown.

Trapezoid

You have correctly determined that the formula for the area of a trapezoid is applicable. The upper half of the figure is a trapezoid with bases 12 ft and 18 ft. Its height will be half the overall height, so will be (1/2)(20 ft) = 10 ft.

The area of the upper half of the figure is ...

A = 1/2(b1 +b2)h

A = 1/2(18 ft +12 ft)(10 ft) = 150 ft²

Whole figure

Since that is half the symmetrical figure, the area of the whole figure is ...

A = 2(150 ft²) = 300 ft²

The area of the figure is 300 square feet.

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Additional comment

There are no markings on the figure to suggest it is symmetrical. However that is an assumption you must make if the area is to be determined.

You can also treat it as a 12 ft by 20 ft rectangle with a 6 ft high triangle that has a base of 20 ft. Doing that, the area calculation is ...

rectangle area + triangle area = (12 ft)(20 ft) + (1/2)(20 ft)(6 ft) = 300 ft²

You may notice that this computation does not require symmetry, except that it does require the bottom edge be 12 ft. The "altitude" line is not constrained to divide the 20 ft side in half.

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User Higigig
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