1. Name a radius.

2. Name a chord.

3. Name a diameter.

4. Find if mACB = 80.

5. Write an equation of the circle with center at (–3, 2) and a diameter of 6.

• height of a parallelogram

• Find perimeters and areas of parallelograms.

• Determine whether points on a coordinate plane define a parallelogram.

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Perimeter and Area of a Parallelogram

Base and Side: Each pair of opposite sides of a parallelogram has the same measure. Each base is 32 inches long, and each side is 24 inches long.

Find the perimeter and area of

Perimeter and Area of a Parallelogram

Divide each side by 2.

Height: Use a 30-60-90 triangle to find the height. Recall that if the measure of the leg opposite the 30 angle is x, then the length of the hypotenuse is 2x, and the length of the leg

opposite the 60 angle is .

Substitute 24 for the hypotenuse.

So, the height of the parallelogram is or inches.

Perimeter: The perimeter of a polygon is the sum of the measures of its sides. So, the perimeter of

or 112 inches.

Perimeter and Area of a Parallelogram

Area: Area of a parallelogram

Answer: The perimeter of is 112 inches, and the area is about 665.1 square inches.

A. A

B. B

C. C

D. D

A. 48 m

B. 45.2 m

C. 96 m

D. 90.4 m

A. Find the perimeter of

A. A

B. B

C. C

D. D

A. 18.2 m2

B. 381.9 m2

C. 567 m2

D. 491.0 m2

B. Find the area of

The Kanes want to sod a portion of their yard. Find the number of square yards of grass needed to sod the shaded region in the diagram.

To find the number of square yards of grass needed, find the number of square yards of the entire lawn and subtract the number of square yards where grass will not be needed. Grass will not be needed for the vegetable garden, the garage, or the house and walkways.

Entire lawn: b = 200 ft, h = 150 ft

Area

Entire LawnVegetable Garden Garage

House and Walkways

Vegetable Garden: b = 50 ft, h = 40 ft

Garage: b = 50 ft, h = 60 ft

House and Walkways: b = 100 ft, h = 60 ft

A = bh

= 200 ● 150

= 30,000 ft2

A = bh

= 50 ● 40

= 2000 ft2

A = bh

= 50 ● 60

= 3000 ft2

A = bh

= 100 ● 60

= 6000 ft2

The total area is 30,000 – 2000 – 3000 – 6000 or 19,000 square feet. There are 9 square feet in one square yard, so divide by 9 to convert from square feet to square yards.

Answer: They will need about 2111 square yards of sod.

1. A

2. B

3. C

4. D

A. 106 yd2

B. 317 yd2

C. 133 yd2

D. 122 yd2

The Wagners are planning to put hardwood floors in their dining room, living room, and kitchen. Find the number of square yards of wood needed. To the nearest whole number.

A. The vertices of a quadrilateral are A(–2, 3), B(4, 1), C(3, –2), and D(–3, 0). Determine whether the quadrilateral is a square, a rectangle, or a parallelogram.

First graph each point and draw the quadrilateral. Then determine the slope of each side.

Perimeter and Area on the Coordinate Plane

Perimeter and Area on the Coordinate Plane

Opposite sides have the same slope, so they are parallel. ABCD is a parallelogram. The slopes of the consecutive sides are negative reciprocals of each other, so the sides are perpendicular. Thus, the parallelogram is a rectangle. In order for the rectangle to be a square, all sides must be equal. Use the Distance Formula to find the side lengths.

Perimeter and Area on the Coordinate Plane

Answer: rectangle

Perimeter and Area on the Coordinate Plane

Since , rectangle ABCD is not a square.

B. Find the perimeter of quadrilateral ABCD.

For the previous question, we found that the figure is a rectangle by proving the opposite sides to be parallel and the consecutive sides to be perpendicular. To show that the figure was not a square, we found that the lengths of consecutive sides were not congruent.

Perimeter and Area on the Coordinate Plane

Add to find the perimeter.

We found that

Since opposite sides are congruent, the lengths of

Definition of perimeter

Perimeter and Area on the Coordinate Plane

Substitution

Simplify radicals.

Add like terms.

Perimeter of

Answer:

C. The vertices of a quadrilateral are A(–2, 3), B(4, 1), C(3, –2), and D(–3, 0). Find the area of quadrilateral ABCD.

Perimeter and Area on the Coordinate Plane

Base: The base is AB, which we found to be .

Height: The height is BC, which we found to be .

Answer: 20 square units

Perimeter and Area on the Coordinate Plane

Simplify.

Multiply.

Area formula

1. A

2. B

3. C

A. square

B. rectangle

C. parallelogram

A. The vertices of a quadrilateral are A(–1, 1), B(1, 4),

C(5, 4), and D(3, 1).

Determine whether the quadrilateral is a square, a rectangle, or a parallelogram.

1. A

2. B

3. C

4. D

A. 14 units

B. 15.21 units

C. 7.61 units

D. 12 units

B. The vertices of a quadrilateral are A(–1, 1), B(1, 4),

C(5, 4), and D(3, 1).

Find the perimeter of quadrilateral ABCD.

1. A

2. B

3. C

4. D

A. 7 units2

B. 14 units2

C. 14.42 units2

D. 12 units2

C. The vertices of a quadrilateral are A(–1, 1), B(1, 4),

C(5, 4), and D(3, 1).

Find the area of quadrilateral ABCD.