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

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

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. Step 7. Answer the question. Vinny has 23.46 square yards in which he can plant.

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

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

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.
• $P=2L+2W$
• The area, $A$ , of a rectangle is the length times the width.
• $A=L\cdot W$
• Triangle Properties
• For any triangle $\Delta ABC$ , the sum of the measures of the angles is 180°.
• $m\angle A+m\angle B+m\angle C=180°$
• 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.
• $A=\frac{1}{2}bh$

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

length of dental floss

living area of an apartment

square

floor space of a bathroom tile

height of a doorway

linear

capacity of a truck trailer

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

1. 10 cm
2. 4 sq. cm

1. 8 cm
2. 3 sq. cm

1. 10 cm
2. 5 sq. cm

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

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

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

1. 58 ft
2. 210 sq. ft

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