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I don't get it and I have tried it multiple ways

I don't get it and I have tried it multiple ways-example-1
User Sam Graham
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1 Answer

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9514 1404 393

Answer:

9350 m²

Explanation:

There are several ways you can go at this. Here are 3 of them:

  1. along an extension of the lower right vertical edge, divide the figure into a rectangle and a right triangle.
  2. 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.
  3. 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

User Marquinho Peli
by
8.3k points

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