Find the perimeter and area of the parallelogram. Round to

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Presentation transcript:

Find the perimeter and area of the parallelogram. Round to the nearest tenth if necessary. 2. Find the perimeter and area of Find the height and base of the parallelogram if the area is 168 square units. Lesson 2 Menu

Find areas of triangles. Find areas of trapezoids and rhombi. Lesson 2 MI/Vocab

Lesson 2 KC1

Find the area of quadrilateral ABCD if AC = 35, BF = 18, and DE = 10. Areas of Triangles Find the area of quadrilateral ABCD if AC = 35, BF = 18, and DE = 10. The area of the quadrilateral is equal to the sum of the areas of Δ Δ ΔADC Area formula Substitution Simplify. Answer: The area of ABCD is 490 square units. Lesson 2 Ex1

Lesson 2 KC2

Area of a Trapezoid on a Coordinate Plane 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. Lesson 2 Ex2

Area of a Trapezoid on a Coordinate Plane Height: Because the bases are horizontal segments, the distance between them can be measured on a vertical line. That is, subtract the y-coordinates. Area: Area of a trapezoid Simplify. Answer: The area of trapezoid RSTU is 19.5 square units. Lesson 2 Ex2

Lesson 2 KC3

Area of a Rhombus on the Coordinate Plane 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. Lesson 2 Ex3

Area of a Rhombus on the Coordinate Plane Solve Use the Distance Formula to find . d1 Use the Distance Formula to find . d2 Lesson 2 Ex3

Area of a Rhombus on the Coordinate Plane Check The area of rhombus MNPR is 15 square units. Answer: 15 square units Lesson 2 Ex3

Find the area of rhombus ABCD with vertices A(–3, 3), B(2, 2), C(3, –3), and D(–2, –2). A. 12 units2 B. 33.9 units2 C. 24 units2 D. 48 units2 A B C D Lesson 2 CYP3

Use the formula for the area of a rhombus and solve for d2. Find Missing Measures Rhombus RSTU has an area of 64 square inches. Find US if RT = 8 inches. Use the formula for the area of a rhombus and solve for d2. Answer: 16 inches Lesson 2 Ex4

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 A B C D Lesson 2 CYP4

Lesson 2 PS1

Area of Congruent Figures 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. Lesson 2 Ex5

Area of Congruent Figures Area of a trapezoid Substitution Add. Multiply. Divide each side by 4.5. Answer: Each trapezoid has a height of 2 feet. Lesson 2 Ex5

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. A. 3 in. B. 6 in. C. 2 in. D. 9 in. A B C D Lesson 2 CYP5