1. 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

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

3. Lesson 2 KC1

4. 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

5. Lesson 2 KC2

6. 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

7. 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

8. Lesson 2 KC3

9. 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

10. 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

11. 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

12. 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 units2
C. 24 units2
D. 48 units2 A B C D
Lesson 2 CYP3

13. 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

14. 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

15. Lesson 2 PS1

16. 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

17. 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

18. 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