1. Find the perimeter and area of the parallelogram. Round to the nearest tenth if necessary.
2. Find the perimeter and area of the parallelogram. Round to the nearest tenth if necessary.
3. Find the height and base of the parallelogram if the area is 168 square units.
Areas of Triangles
Find the area of quadrilateral ABCD if AC = 35, BF = 18, and DE = 10.
Answer: The area of ABCD is 490 square units.
Substitution
Simplify.
Area formula
The area of the quadrilateral is equal to the sum of the areas of Δ Δ
Δ ΔADC
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.
Area of a Trapezoid on a Coordinate Plane
Answer: The area of trapezoid RSTU is 19.5 square units.
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.
Area of a trapezoid
Simplify.
Find the area of rhombus MNPR with vertices at M(0, 1), N(4, 2), P(3, –2), and R(–1, –3).
Area of a Rhombus on the Coordinate Plane
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.
Area of a Rhombus on the Coordinate Plane
Use the Distance Formula to find .
Use the Distance Formula to find .Solve
d1
d2
Answer: 15 square units
Area of a Rhombus on the Coordinate Plane
Check The area of rhombus MNPR is 15 square units.
Area of a rhombus
1. A2. B3. C4. D
A. 12 units2
B. 33.9 units2
C. 24 units2
D. 48 units2
Find the area of rhombus ABCD with vertices A(–3, 3), B(2, 2), C(3, –3), and D(–2, –2).
Rhombus RSTU has an area of 64 square inches. Find US if RT = 8 inches.
Find Missing Measures
Answer: 16 inches
Use the formula for the area of a rhombus and solve for d2.
A. AB. BC. CD. D
A. 3 yd
B. 6 yd
C. 2.1 yd
D. 7 yd
Trapezoid QRST has an area of 210 square yards. Find the height of QRST.
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.
Area of Congruent Figures
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 Congruent Figures
Area of a trapezoid
Substitution
Add.
Multiply.
Divide each side by 4.5.
A. AB. BC. CD. D
A. 3 in.
B. 6 in.
C. 2 in.
D. 9 in.
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.
