11-2 areas of trapezoids, 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.

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

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

trapezoid

rhombus,

parallelogram

rectangle, parallelogram

trapezoid

square, rectangle, rhombus, parallelogram

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

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

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. 288 ft2

B. 295.5 ft2

C. 302.5 ft2

D. 310 ft2

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

Definitions

• Rhombus: a quadrilateral with all four sides congruent.

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

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

p. 791

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 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

A. 48.75 ft2

B. 58.5 ft2

C. 75.25 ft2

D. 117 ft2

A. Find the area of the kite.

A. 45 in2

B. 90 in2

C. 180 in2

D. 360 in2

B. Find the area of the rhombus.

p. 792

Area Formulas

11-2 Assignment

Page 793, 8-16No formulas with

numbers in it, no credit