11-2 areas of trapezoids, rhombi, and kites you found areas of triangles and parallelograms. find...

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11-2 Areas of Trapezoids, Rhombi, and Kites You found areas of triangles and parallelograms. • Find areas of trapezoids. • Find areas of rhombi and kites.

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Page 1: 11-2 Areas of Trapezoids, Rhombi, and Kites You found areas of triangles and parallelograms. Find areas of trapezoids. Find areas of rhombi and kites

11-2 Areas of Trapezoids, Rhombi, and Kites

You found areas of triangles and parallelograms.

• Find areas of trapezoids.

• Find areas of rhombi and kites.

Page 2: 11-2 Areas of Trapezoids, Rhombi, and Kites You found areas of triangles and parallelograms. Find areas of trapezoids. Find areas of rhombi and kites

DefinitionsA rhombus is a quadrilateral

with four congruent sides.

(All rhombuses are parallelograms.)

A trapezoid is a quadrilateral with exactly one pair of parallel sides. The parallel sides are the bases of the trapezoid, and the nonparallel sides are its legs.

base

base

legleg

Page 3: 11-2 Areas of Trapezoids, Rhombi, and Kites You found areas of triangles and parallelograms. Find areas of trapezoids. Find areas of rhombi and kites

Classify each quadrilateral as a square, rectangle, rhombus, parallelogram or trapezoid.

trapezoid

rhombus,

parallelogram

rectangle, parallelogram

trapezoid

square, rectangle, rhombus, parallelogram

Page 4: 11-2 Areas of Trapezoids, Rhombi, and Kites You found areas of triangles and parallelograms. Find areas of trapezoids. Find areas of rhombi and kites

The area of a trapezoid is the product of half the sum of the bases (b1 and b2) and the height (h).

hbb

A2

21 hbbA 212

1

Page 5: 11-2 Areas of Trapezoids, Rhombi, and Kites You found areas of triangles and parallelograms. Find areas of trapezoids. Find areas of rhombi and kites

Find the area of the trapezoid

47.5 cm2

9

4.5

5.5

37.125

5 cm

14 cm

5 cm2

6

8

30

Page 6: 11-2 Areas of Trapezoids, Rhombi, and Kites You found areas of triangles and parallelograms. Find areas of trapezoids. Find areas of rhombi and kites

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

Page 7: 11-2 Areas of Trapezoids, Rhombi, and Kites You found areas of triangles and parallelograms. Find areas of trapezoids. Find areas of rhombi and kites

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.

Page 8: 11-2 Areas of Trapezoids, Rhombi, and Kites You found areas of triangles and parallelograms. Find areas of trapezoids. Find areas of rhombi and kites

Definitions

• Rhombus: a quadrilateral with all four sides congruent.

• Kite: a quadrilateral with exactly two pairs of consecutive congruent sides.

Page 9: 11-2 Areas of Trapezoids, Rhombi, and Kites You found areas of triangles and parallelograms. Find areas of trapezoids. Find areas of rhombi and kites

The area of a rhombus or kite is ½ of the product of diagonal 1 and diagonal 2.

p. 791

Page 10: 11-2 Areas of Trapezoids, Rhombi, and Kites You found areas of triangles and parallelograms. Find areas of trapezoids. Find areas of rhombi and kites

A. Find the area of the kite.

Area of a kite

d1 = 7 and d2 = 12

Answer: 42 ft2

Page 11: 11-2 Areas of Trapezoids, Rhombi, and Kites You found areas of triangles and parallelograms. Find areas of trapezoids. Find areas of rhombi and kites

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.

Answer: 126 in2

Area of a rhombus

Step 2 Find the area of the rhombus.

d1 = 14 and d2 = 18

Simplify.2

Page 12: 11-2 Areas of Trapezoids, Rhombi, and Kites You found areas of triangles and parallelograms. Find areas of trapezoids. Find areas of rhombi and kites

A. 48.75 ft2

B. 58.5 ft2

C. 75.25 ft2

D. 117 ft2

A. Find the area of the kite.

Page 13: 11-2 Areas of Trapezoids, Rhombi, and Kites You found areas of triangles and parallelograms. Find areas of trapezoids. Find areas of rhombi and kites

A. 45 in2

B. 90 in2

C. 180 in2

D. 360 in2

B. Find the area of the rhombus.

Page 14: 11-2 Areas of Trapezoids, Rhombi, and Kites You found areas of triangles and parallelograms. Find areas of trapezoids. Find areas of rhombi and kites

p. 792

Area Formulas

Page 15: 11-2 Areas of Trapezoids, Rhombi, and Kites You found areas of triangles and parallelograms. Find areas of trapezoids. Find areas of rhombi and kites

11-2 Assignment

Page 793, 8-16No formulas with

numbers in it, no credit

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