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

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.

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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.
    • $P=2L+2W$
  • 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°.
    • $m\angle A+m\angle B+m\angle C=\mathrm{180°}$
  • 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.

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

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1. ⓐ 8 cm
2. ⓑ 3 sq. cm

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1. ⓐ 10 cm
2. ⓑ 5 sq. cm

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Use the Properties of Rectangles

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