11.2

Warm UpWarm Up

Lesson QuizLesson Quiz

Lesson PresentationLesson Presentation

Areas of Trapezoids, Rhombuses, and Kites

11.2 Warm-Up

1. Find the area of a parallelogram with height 12 feet and base 8 feet.

2. Find the area of an isosceles triangle with sides 20, 20, and 24 units.

ANSWER 96 ft2

ANSWER 192 square units

11.2 Warm-Up

3. What is the length of the midsegment of a trapezoid with bases 10 inches and 15 inches?

4. Solve 200 =12 x (18 + 22).

ANSWER 12.5 in.

ANSWER 10

11.2 Example 1

BASKETBALL The free-throw lane on an international basketball court is shaped like a trapezoid. Find the area of the free-throw lane.

11.2 Example 1

SOLUTION

The height of the trapezoid is 5.8 meters. The lengths of the bases are 3.6 meters and 6 meters.

A = h(b1 + b2)12

= (5.8)(3.6 + 6)12

= 27.84

Formula for area of a trapezoid

Substitute 5.8 for h, 3.6 for b1, and6 for b2.

Simplify.

The area of the free-throw lane is about 27.8 square meters.

11.2 Example 2

MUSIC Rhombus PQRS represents one of the inlays on a guitar. Find the area of the inlay.

STEP 1 Find the length of each diagonal. The diagonals of a rhombus bisect each other, so QN = NS and PN = NR.

QS = QN + NS = 9 + 9 = 18 mm

PR = PN + NR = 12 + 12 = 24 mm

SOLUTION

11.2 Example 2

STEP 2 Find the area of the rhombus. Let d1

represent QS and d2 represent PR.

A = d1d212

= (18)(24)12

= 216

Formula for area of a rhombus

Substitute.

Simplify.

The area of the inlay is 216 square millimeters.

11.2 Guided Practice

Find the area of the figure.

1.

28 ft2ANSWER

11.2 Guided Practice

Find the area of the figure.

42 in.2ANSWER

2.

11.2 Guided Practice

Find the area of the figure.

2400 m2ANSWER

3.

11.2 Example 3

SOLUTION

Draw and label a diagram. Let x be the length of one diagonal. The other diagonal is twice as long, so label it 2x. Use the formula for the area of a kite to find the value of x.

11.2 Example 3

A = d1d212

72.25 = (x)(2x)12

Formula for area of a kite

Substitute 72.25 for A, x for d1, and 2x for d2.

72.25 = x2 Simplify.

8.5 = x Find the positive square root of each side.

The lengths of the diagonals are 8.5 inches and 2(8.5) = 17 inches.

The correct answer is C. ANSWER

11.2 Example 4

City Planning You have a map of a city park. Each grid square represents a 10 meter by 10 meter square. Find the area of the park.

11.2 Example 4

SOLUTION

STEP 1 Find the lengths of the bases and the height of trapezoid ABCD.

b1 = BC = 70 – 30

b2 = AD = 80 – 10

h = BE = 60 – 10

= 40 m

= 70 m

= 50 m

STEP 2 Find the area of ABCD.

A = h(b1 + b2)12

12= (50)(40 + 70) = 2750

The area of the park is 2750 square meters.

11.2 Guided Practice

4. The area of a kite is 80 square feet. One diagonal is 4 times as long as the other. Find the diagonal lengths.

d1 = 2 √10 ft, d2 = 8 √10 ft

ANSWER

5. Find the area of a rhombus with vertices M(1, 3), N(5, 5), P(9, 3), and Q(5, 1).

16 units2

ANSWER

11.2 Lesson Quiz

ANSWER 20 square units

1.

Find the area of each figure.

11.2 Lesson Quiz

2.

ANSWER 144 cm2

Find the area of each figure.

11.2 Lesson Quiz

Find the area of each figure.

ANSWER 135 ft2

3.

11.2 Lesson Quiz

Find the area of each figure.

4.

ANSWER 1072 ft2

11.2 Lesson Quiz

5. The height of a trapezoid is 8 feet. One base is twice as long as the other, and the area is 72 square feet. How long is each base?

ANSWER 6 ft; 12 ft