Five-Minute Check (over Lesson 11–1)

NGSSS

Then/Now

New Vocabulary

Key Concept: Area of a Trapezoid

Example 1: Real-World Example: Area of a Trapezoid

Example 2: Standardized Test Example

Key Concept: Area of a Rhumbus or Kite

Example 3: Area of a Rhombus and a Kite

Example 4: Use Area to Find Missing Measures

Concept Summary: Areas of Polygons

Over Lesson 11–1

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 48 cm

B. 56 cm

C. 101.1 cm

D. 110 cm

Find the perimeter of the figure. Round

to the nearest tenth if necessary.

Over Lesson 11–1

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 37.9 ft

B. 40 ft

C. 43.9 ft

D. 45 ft

Find the perimeter of the figure. Round

to the nearest tenth if necessary.

Over Lesson 11–1

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 58 in2

B. 83 in2

C. 171.5 in2

D. 180 in2

Find the area of the figure. Round to the nearest tenth if necessary.

Over Lesson 11–1

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 90 m2

B. 62 m2

C. 5 m2

D. 3.4 m2

Find the area of the figure. Round to the nearest tenth if necessary.

Over Lesson 11–1

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 11 units; 13 units

B. 12 units; 14 units

C. 13 units; 15 units

D. 14 units; 16 units

Find the height and base of the parallelogram if the area is 168 square units.

Over Lesson 11–1

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 2.1 centimeters

B. 4.2 centimeters

C. 8.4 centimeters

D. 16.8 centimeters

The area of an obtuse triangle is 52.92 square centimeters. The base of the triangle is 12.6 centimeters. What is the height of the triangle?

MA.912.G.2.5 Explain the derivation and apply formulas for perimeter and area of polygons.

MA.912.G.2.6 Use coordinate geometry to prove properties of congruent, regular and similar polygons, and to perform transformations in the plane.

You found areas of triangles and parallelograms. (Lesson 11–1)

• Find areas of trapezoids.

• Find areas of rhombi and kites.

• height of a trapezoid

Area of a Trapezoid

SHAVING Find the area of steel used to make the side of the razor blade shown below.

Area of a trapezoid

h = 1, b1 = 3, b2 = 2.5

Simplify.

Answer: A = 2.75 cm2

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 288 ft2

B. 295.5 ft2

C. 302.5 ft2

D. 310 ft2

Find the area of the side of the pool outlined below.

OPEN ENDED Miguel designed a deck shaped like the trapezoid shown below. Find the area of the deck.

Read the Test Item

You are given a trapezoid with one base measuring 4 feet, a height of 9 feet, and a third side measuring 5 feet. To find the area of the trapezoid, first find the measure of the other base.

Solve the Test Item

Draw a segment to form a right triangle and a rectangle. The triangle has a hypotenuse of 5 feet and legs of ℓ and 4 feet. The rectangle has a length of 4 feet and a width of x feet.

Use the Pythagorean Theorem to find ℓ.

a2 + b2 = c2 Pythagorean Theorem

42 + ℓ2 = 52 Substitution

16 + ℓ2 = 25 Simplify.

ℓ2 = 9 Subtract 16 from each side.

ℓ = 3 Take the positive square rootof each side.

By Segment Addition, ℓ + x = 9. So, 3 + x = 9 and x = 6. The width of the rectangle is also the measure of the second base of the trapezoid.

Area of a trapezoid

Substitution

Simplify.

Answer: So, the area of the deck is 30 square feet.

Check

The area of the trapezoid is the sum of the areas of

the areas of the right triangle and rectangle. The area

of the triangle is or 6 square feet. The area of

the rectangle is (4)(6) or 24 square feet. So the area of

the trapezoid is 6 + 24 or 30 square feet.

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 58 ft2

B. 63 ft2

C. 76 ft2

D. 88 ft2

Ramon is carpeting a room shaped like the trapezoid shown below. Find the area of the carpet needed.

Area of a Rhombus and a Kite

A. Find the area of the kite.

Area of a kite

d1 = 7 and d2 = 12

Answer: 42 ft2

Area of a Rhombus and a Kite

B. Find the area of the rhombus.

Step 1 Find the length of each diagonal.

Since the diagonals of a rhombus bisecteach other, then the lengths of thediagonals are 7 + 7 or 14 in. and 9 + 9 or 18 in.

Area of a Rhombus and a Kite

Answer: 126 in2

Area of a rhombus

Step 2 Find the area of the rhombus.

d1 = 14 and d2 = 18

Simplify. 2

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 48.75 ft2

B. 58.5 ft2

C. 75.25 ft2

D. 117 ft2

A. Find the area of the kite.

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 45 in2

B. 90 in2

C. 180 in2

D. 360 in2

B. Find the area of the rhombus.

Use Area to Find Missing Measures

ALGEBRA One diagonal of a rhombus is half as long as the other diagonal. If the area of the rhombus is 64 square inches, what are the lengths of the diagonals?

Step 1 Write an expression to represent each measure. Let x represent the length of one diagonal. Then the length of the other diagonal is x.__1

2

Use Area to Find Missing Measures

Step 2 Use the formula for the area of a rhombus to find x.

Area of a rhombus

A = 64, d1= x, d2= x__  12

Simplify.

256 = x2 Multiply each side by 4.

16 = x Take the positive square root of each side.

Use Area to Find Missing Measures

Answer: So, the lengths of the diagonals are 16 inches

and (16) or 8 inches. __12

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 3 yd

B. 6 yd

C. 2.1 yd

D. 7 yd

Trapezoid QRST has an area of 210 square yards. Find the height of QRST.