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Five-Minute Check (over Lesson 111) CCSS Then/Now

New Vocabulary Key Concept Area of a

Trapezoid Example 1 Real-World Example Area of

a Trapezoid Example 2 Standardized Test Example

Area of a Trapezoid 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

5-Minute Check 1

Find the perimeter of the figure. Round to the

nearest tenth if necessary.

A. 48 cm B. 56 cm C. 101.1 cm D. 110 cm

5-Minute Check 2

Find the perimeter of the figure. Round to the

nearest tenth if necessary.

A. 37.9 ft B. 40 ft C. 43.9 ft D. 45 ft

5-Minute Check 3

Find the area of the figure. Round to the

nearest tenth if necessary.

A. 58 in2 B. 83 in2 C. 171.5 in2 D. 180 in2

5-Minute Check 4

Find the area of the figure. Round to the

nearest tenth if necessary.

A. 9.0 m2 B. 62 m2 C. 5 m2 D. 3.4 m2

5-Minute Check 5

Find the height and base of the parallelogram if

the area is 168 square units.

A. 11 units 13 units B. 12 units 14 units C. 13

units 15 units D. 14 units 16 units

5-Minute Check 6

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?

A. 2.1 centimeters B. 4.2 centimeters C. 8.4

centimeters D. 16.8 centimeters

CCSS

Content Standards G.MG.3 Apply geometric methods

to solve problems (e.g., designing an object or

structure to satisfy physical constraints or

minimize cost working with typographic grid

systems based on ratios). Mathematical

Practices 1 Make sense of problems and persevere

in solving them. 7 Look for and make use of

structure.

Then/Now

You found areas of triangles and parallelograms.

- Find areas of trapezoids.

- Find areas of rhombi and kites.

Vocabulary

- height of a trapezoid

Concept 1

Example 1

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

Example 1

Find the area of the side of the pool outlined

below.

A. 288 ft2 B. 295.5 ft2 C. 302.5 ft2 D. 310 ft2

Example 2

Area of a Trapezoid

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.

Example 2

Area of a Trapezoid

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.

Example 2

Area of a Trapezoid

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 root of each side.

Example 2

Area of a Trapezoid

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.

Example 2

Area of a Trapezoid

Check

Example 2

Ramon is carpeting a room shaped like the

trapezoid shown below. Find the area of the

carpet needed.

A. 58 ft2 B. 63 ft2 C. 76 ft2 D. 88 ft2

Concept 2

Example 3A

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

Example 3B

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 bisect each other,

then the lengths of the diagonals are 7 7 or

14 in. and 9 9 or 18 in.

Example 3B

Area of a Rhombus and a Kite

Step 2 Find the area of the rhombus.

Area of a rhombus

d1 14 and d2 18

Answer 126 in2

Example 3A

A. Find the area of the kite.

A. 48.75 ft2 B. 58.5 ft2 C. 75.25 ft2 D. 117 ft2

Example 3B

B. Find the area of the rhombus.

A. 45 in2 B. 90 in2 C. 180 in2 D. 360 in2

Example 4

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?

Example 4

Use Area to Find Missing Measures

Step 2 Use the formula for the area of a rhombus

to find x.

Area of a rhombus

Simplify.

256 x2 Multiply each side by 4.

16 x Take the positive square root of each

side.

Example 4

Use Area to Find Missing Measures

Example 4

Trapezoid QRST has an area of 210 square yards.

Find the height of QRST.

A. 3 yd B. 6 yd C. 2.1 yd D. 7 yd

Concept 3

End of the Lesson