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Lesson 11.2 Key Notes

• Area of a Triangle:

• Area of a Trapezoid:

• Area of a Rhombus:

• Postulate 11.1 Congruent figures have equal areas

bhA2

1

)(2

121 bbhA

212

1ddA

Substitution

Simplify.

The area of the quadrilateral is equal to the sum of the areas of

Find the area of quadrilateral ABCD if AC 35, BF 18, and DE 10.

Area formula

Answer: The area of ABCD is 490 square units.

Find the area of quadrilateral HIJK ifand

Answer:

Find the area of trapezoid RSTU with vertices R(4, 2), S(6, –1), T(–2, –1), and U(–1, 2).

Bases: Since and are horizontal, find their length by subtracting the x-coordinates of their endpoints.

Area:

Height: Because the bases are horizontal segments, the distance between them can be measured on a vertical line. That is, subtract the y-coordinates.

Answer: The area of trapezoid RSTU is 19.5 square units.

Area of a trapezoid

Simplify.

Find the area of trapezoid WXYZ with vertices W(–3, 0), X(1, 0), Y(2, –3), and Z(–5, –3).

Answer:

Find the area of rhombus MNPR with vertices at M(0, 1), N(4, 2), P(3, –2), and R(–1, –3).

Explore To find the area of the rhombus, we need to know the lengths of each diagonal.

Plan Use coordinate geometry to find the length of each diagonal. Use the formula to find the area of rhombus MNPR.

Use the Distance Formula to find .

Use the Distance Formula to find .Solve

Examine The area of rhombus MNPR is 15 square units.

Area of a rhombus

Answer: 15 square units

Find the area of rhombus ABCD with vertices A(–3, 3), B(2, 2), C(3, –3), and D(–2, –2).

Answer:

Use the formula for the area of a rhombus and solve for d2.

Rhombus RSTU has an area of 64 square inches. Find if inches.

Answer: US is 16 inches long.

Trapezoid DEFG has an area of 120 square feet. Find the height of DEFG.

Answer: The height of trapezoid DEFG is 8 feet.

Use the formula for the area of a trapezoid and solve for h.

Answer: 6 yd

Answer: 27 cm

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

a. Rhombus ABCD has an area of 81 square centimeters. Find BD if centimeters.

STAINED GLASS This stained glass window is composed of 8 congruent trapezoidal shapes. The total area of the design is 72 square feet. Each trapezoid has bases of 3 and 6 feet. Find the height of each trapezoid.

First, find the area of one trapezoid. From Postulate 11.1, the area of each trapezoid is the same. So, the area of each trapezoid is or 9 square feet.

Next, use the area formula to find the height of each trapezoid.

Answer: Each trapezoid has a height of 2 feet.

Area of a trapezoid

Substitution

Add.

Multiply.

Divide each side by 4.5.

INTERIOR DESIGN This window hanging is composed of 12 congruent trapezoidal shapes. The total area of the design is 216 square inches. Each trapezoid has bases of 4 and 8 inches. Find the height of each trapezoid.

Answer: 3 in.

HW #1: p. 598 10-22 evens, 27-30 all (11 problems)

HW #2: p. 606 14-34 evens (11 problems)