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9.4 Use properties of rectangles, triangles, and trapezoids  (Page 8/17)

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The height of a trapezoid is 7 centimeters and the bases are 4.6 and 7.4 centimeters. What is the area?

42 sq. cm

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The height of a trapezoid is 9 meters and the bases are 6.2 and 7.8 meters. What is the area?

63 sq. m

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Vinny has a garden that is shaped like a trapezoid. The trapezoid has a height of 3.4 yards and the bases are 8.2 and 5.6 yards. How many square yards will be available to plant?

Solution

Step 1. Read the problem. Draw the figure and label it with the given information. .
Step 2. Identify what you are looking for. the area of a trapezoid
Step 3. Name. Choose a variable to represent it. Let A = the area
Step 4. Translate.
Write the appropriate formula.
Substitute.
.
Step 5. Solve the equation. .
Step 6. Check: Is this answer reasonable?
Yes. The area of the trapezoid is less than the area of a rectangle with a base of 8.2 yd and height 3.4 yd, but more than the area of a rectangle with base 5.6 yd and height 3.4 yd.
This image is a table with two rows. the first row is split into three columns. The first column is the formula Area of a rectangle equals base times height. On the next line under this it has numbers plugged into the formula; the base, 8.2 in parentheses times the height 3.4 in parentheses. Under this is it has “equals 27.88 yards squared”. The center column includes the formula of a trapezoid and says Area of a trapezoid equals one half times 3.5 yards in parentheses times 5.8 plus 8.2 in parentheses. Under this it has “equals 23.46 yards squared”. In the third column it it has the formula the area of a rectangle equals base times height. Under this it has equals 5.6 in parentheses times 3.4 in parentheses. Under this it has “equals 19.04 yards squared.” In the second row, centered from left to right it has “Area of a rectangle” and a “greater than” sign, “Area of a trapezoid” and a greater than sign and “area of a rectangle”. Under Area of a rectangle it has 27.88, then 23.46 under “area of a trapezoid”, then 19.04 under “area of a rectangle”.
Step 7. Answer the question. Vinny has 23.46 square yards in which he can plant.
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Lin wants to sod his lawn, which is shaped like a trapezoid. The bases are 10.8 yards and 6.7 yards, and the height is 4.6 yards. How many square yards of sod does he need?

40.25 sq. yd

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Kira wants cover his patio with concrete pavers. If the patio is shaped like a trapezoid whose bases are 18 feet and 14 feet and whose height is 15 feet, how many square feet of pavers will he need?

240 sq. ft

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The Links to Literacy activity Spaghetti and Meatballs for All will provide you with another view of the topics covered in this section."

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Key concepts

  • Properties of Rectangles
    • Rectangles have four sides and four right (90°) angles.
    • The lengths of opposite sides are equal.
    • The perimeter, P , of a rectangle is the sum of twice the length and twice the width.
      • P = 2 L + 2 W
    • The area, A , of a rectangle is the length times the width.
      • A = L ⋅ W
  • Triangle Properties
    • For any triangle Δ A B C , the sum of the measures of the angles is 180°.
      • m ∠ A + m ∠ B + m ∠ C = 180°
    • The perimeter of a triangle is the sum of the lengths of the sides.
      • P = a + b + c
    • The area of a triangle is one-half the base, b, times the height, h.
      • A = 1 2 b h

Practice makes perfect

Understand Linear, Square, and Cubic Measure

In the following exercises, determine whether you would measure each item using linear, square, or cubic units.

amount of water in a fish tank

cubic

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length of dental floss

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living area of an apartment

square

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floor space of a bathroom tile

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height of a doorway

linear

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capacity of a truck trailer

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In the following exercises, find the ⓐ perimeter and ⓑ area of each figure. Assume each side of the square is 1 cm.

A rectangle is shown comprised of 4 squares forming a horizontal line.

  1. ⓐ 10 cm
  2. ⓑ 4 sq. cm

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A rectangle is shown comprised of 3 squares forming a vertical line.
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Three squares are shown. There is one on the bottom left, one on the bottom right, and one on the top right.

  1. ⓐ 8 cm
  2. ⓑ 3 sq. cm

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Four squares are shown. Three form a horizontal line, and there is one above the center square.
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Five squares are shown. There are three forming a horizontal line across the top and two underneath the two on the right.

  1. ⓐ 10 cm
  2. ⓑ 5 sq. cm

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A square is shown. It is comprised of nine smaller squares.
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Use the Properties of Rectangles

In the following exercises, find the ⓐ perimeter and ⓑ area of each rectangle.

The length of a rectangle is 85 feet and the width is 45 feet.

  1. ⓐ 260 ft
  2. ⓑ 3825 sq. ft

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The length of a rectangle is 26 inches and the width is 58 inches.

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A rectangular room is 15 feet wide by 14 feet long.

  1. ⓐ 58 ft
  2. ⓑ 210 sq. ft

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Questions & Answers

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Source:  OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9
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