Geometry 1

To sod a yard 100 feet by 60 feet would require how many square feet of sod?

100 x 60 = 6000 square feet

Find the perimeter of a picture that measures 11 by 12 inches

11 x 2 = 22 12 x 2 = 24 22 + 24 = 46 inches

Find the perimeter of a triangle having two sides of 12.3 centimeters and a base of 5.7 centimeters

12.3 + 12.3 + 5.7 = 30. 3 centimeters

. A triangular-shaped park whose base is 120 feet and whose height is 90 feet is going to be sodded at a cost of 53¢ per square foot. How much is it going to cost to sod the whole park?

120 * 90 = 10,800 10,800 * 1/2 = 5400 5400 * .53 = $2862

A bin that measures 16 feet on each side is filled with grain. How many cubic feet of grain does it hold

16 * 16 * 16 = 4096 cubic feet

A triangular piece of land has two sides 196 feet and one side of 100 feet. How much fencing will be required to enclose it

196 + 196 + 100 = 492 feet

How many feet of fencing will Joseph need to fence a rectangular garden that is 200 feet by 150 feet

200 x 2 = 400 150 x 2 = 300 400 + 300 =700 feet

How much more area does a triangle with a base of 24 and a height of 20 have than a triangle with a base of 22 and a height of 18?

24 * 20 = 480 ÷2 = 240 22 * 18 = 396 ÷ 2 = 198 240 - 198 = 42 square units

A circular rose garden is 6 feet across. What is the area of the garden?

28.26 ft²

A square sandbox that is 3 feet long and 3 feet deep, will hold how many cubic feet of sand?

3 * 3 * 3 = 27 cu. feet

Find the volume of a box that is 5 feet long, 4 feet wide, and 2 feet high.

5 * 4 * 2 = 40 cu. Feet

How much braid is needed to go around a tablecloth that is 62 by 80 inches?

62 x 2 = 124 80 x 2 = 160 124 + 160 = 284 inches

Area of a trapezoid

A = 1/2 * (base1 + base2) * height

Area of a triangle

A = 1/2 * base * height

Area of a Parallelogram

A = base * height or A = bh

Find the area of a room that measures 12 feet by 10 feet.

A = length * width A = 12 * 10 A = 120 square feet

Volume of a Rectangular Container

A rectangular solid is a 3 dimensional shape that has rectangles for its 6 sides. V = lwh

A circular pool at the zoo for the polar bears has a radius of 14 feet. How much fencing is needed to enclose the pool

C = 3.14 * diameter diameter = 14 * 2 = 28 C = 3.14 * 28 = 87.92 feet

Area of Square

L*W

Perimeter of a Rectangle

P = 2 * length + 2 * width

Area of a circle

The formula for finding the area of a circle is: A = * radius2 or A = r2

diameter

diameter is a line segment going across the circle passing through the center point. It divides the circle into two equal parts—called semicircles. The diameter is twice the radius.

The perimeter of a square room is 32 feet. What is the length of each side of the room?

s = P/4 s = 32/4 s = 8 feet Each side of the room is 8 feet long.

Find the perimeter of a square whose sides are 2/3 inch long

. 2 2/3 inches

The ends of an A-frame house each have a base of 26 feet and a height of 16 feet. What is the total area of both ends?

. 26 * 16 = 416 416 * 1/2 = 208 208 * 2 = 416 feet2

What is the perimeter of a square picture that is 11 inches on each side?

. 44 inches

Pete has a train set. The track is circular and has a diameter of 7 feet. What is the distance around the track

. C = 3.14 * 7 = 21.98 feet

A barrel stands 5 feet high and has a radius of 2 feet. What is its volume?

. V = 3.14 * 2 * 2 * 5= 62.8 cu. ft.

What is the perimeter of a square picture that is 11 inches on each side?

1. 44 inches

. Find the volume of a trash bin that measures 1.5 meters by 2 meters by 4 meters.

1/5 * 2 * 4 = 12 cu. meters

What is the volume of a cube that has a side of 10 yards?

10 * 10 * 10 = 1000 yds3

How much paint will a painter need to cover a wall that is in the shape of a parallelogram? The base of the wall is 12 feet and the height is 9 feet?

10 * 4.5 = 45 square feet

How long is each side of a square room that has a perimeter of 48 feet?

12 feet

Find the area of a square having a side of 12 centimeters

12 x 12 = 144 sq centimeters

How many square yards of carpet will be needed to carpet a room that is 12 feet by 30 feet? (1sq. yd. = 9 sq. ft.)

12 x 30 = 360 square feet 360 ÷ 9 = 40 square yards

A fertilizer company recommends 1 bag of fertilizer per 1000 square feet of lawn. How many bags of fertilizer will be needed for a lawn that is 75 feet by 125 feet?

125 x 75 = 9375 square feet 9375 ÷ 1000 = 9.375 bags You would need to buy 10 bags

What size square painting will fit inside an antique frame with a perimeter of 56 inches?

14 inches

How many square feet in a square that measures 3 feet by 3 feet?

3 x 3 = 9 square feet

The radius of a circle of 10 feet. Find the area

314 ft ²

What is the perimeter of a square garden that measures 9 feet on one side?

36 feet

What is the area of a parallelogram that has a base of 37 meters and a height of 26 meters?

37 * 26 = 962 square meters

Find the area of a triangle with a base of 4 miles and a height of 7 miles.

4 * 7 = 28 28 * 1/2 = 14 square miles

A rectangular measuring 40 feet by 6 feet is filled with water 1 foot from the top. How many cubic feet of water does the tank hold if it is 8 feet deep?

40 * 6 * 7 =1680 cu. Feet

The basement of the Johnson's house is in the shape of a trapezoid. If the parallel sides have lengths of 40 and 36 feet, and the distance between the parallel sides is 20 feet, what is the area of the basement?

40 + 36 = 76 ½ * 76 = 38 38 * 20 = 760 sq. feet

. The distance from the center of a circular pool to the edge is 12 feet. Find the area.

452.16 sq.ft

A roofing company is going to shingle a section of a roof that is in the shape of a trapezoid. The parallel sides measure 54 feet and 42 feet, and are 22 feet apart. Find the area of that section of the roof.

54 + 42 = 96 ½ * 96 = 48 48 * 22 = 1056 ft.2

Jeremy has a rectangular plot of land that measures 6 meters by 12 meters. What is the area of this land?

6 x 12 = 72 square meters

Area of a Rectangle

A = length * width

Find the area of a square with a side that is 7 inches long.

A = side2 A = 7 x 7 A = 49 square inches

Volume of a cone

A cone is a 3-dimensional figure with a circular base and sides that meet at a point. Think of a party hat and you've got a cone—or an ice cream cone. The formula for finding volume of a cone is: Volume = 1/3 * * radius2* height This is like the volume of a cylinder formula, but you take 1/3 of the answer. Example: Look at the cone above and let's figure the volume by substituting the values into the formula. V= 1/3 * * radius² * height V = 1/3 * 3.14 * 3² * 9 V = 1/3 * 3.14 * 9 * 9 V = 9 * 9 = 81 1/3 * 81 = 27 27 * 3.14= 84.78 cu. in.

Volume of a Cube

A cube is a three-dimensional figure made up of 6 sides that are squares. The formula for finding volume of a cube is: V = edge3 It is read " volume equals edge cubed or to the third power." To cube a number, multiple it times itself two times.

Volume of a cylinder

A cylinder is a 3-dimensional shape that has a circle as the top and bottom surface. The distance between the top and bottom is called the height of the cylinder. A cylinder is the shape of a tin can. The formula for finding the volume of a cylinder is: V = * r² * height or V = r2h

Volume of a square pyramid

A square pyramid is a shape that has a square for the base and four equal triangular sides that meet at a point. The formula for finding the volume of a square pyramid is: V = 1/3 * (base edge)2 * height

Larry left home and walked 3.75 blocks due west, then 3.3 blocks due south to arrive at a friend's house. He wants to take a shortcut home. About how far is his home from a friend's home - in a straight line?

Let's round the numbers to make them easier to deal with: 3.75 = 4 3.3 = 3 This forms a right triangle. To find the hypotenuse of a right triangle, use this formula: A2 + B2 = C2 Find the square root of the answer: A2 + B2 = C2 (A x A) + (B x B) = (C x C) (4 x 4) + (3 x 3) = C2 16 + 9 = 25 Answer: Larry will walk 5 blocks if he cuts across town.

Perimeter of a Triangle

P = side1 + side2 + side 3

Circumference of a circle

The circumference is the distance around the outside of a circle. It is the same thing as perimeter, but on a circle it is called circumference. Finding the circumference of a circle is a little harder than finding the perimeter of a sided figure. With a sided figure, all you have to do is add the lengths of the sides together. With a circle, you have to use a formula of find the circumference. If you look under the perimeter formulas on the formula, you will see the circle formula listed.

What is the volume of a pyramid with a base that is 5 by 5 and a height of 12 meters?

V = 1/3 * 5 * 5 * 12 1/3 * 25 * 12 1 * 25 * 12 = 100 m³ 3 1 1

A pyramid has a square base with one edge of 9 centimeters and a height of 18.25 centimeters. What is the volume of the pyramid?

V = 1/3 * 9 * 9 * 18.25 1/3 * 81 = 27 27 * 18.25 = 492.75 cu. cm

What is the volume of a can of tomato juice that has a diameter of 2 inches and a height of 7 inches?

V = 3.14 * 1 * 1 * 7 = 21.98 cu. in. (Don't forget to take half of the diameter to find the radius)

Find the volume of a cylinder having a radius of 10 yards and a height of 8 yards.

V = 3.14 * 10 * 10 * 8 = 2512 cu. yds.

A circular goldfish pond has a diameter of 28 feet. How many cubic feet of water does it take to fill the pond to a depth of 2 feet?

V = 3.14 * 14 * 14 * 2 = 1230.88 ft³

Volume

is the amount of space inside a three dimensional object. For instance, think of the space inside of a milk carton. Area involves two-dimensional flat objects and has two dimensions -length and width. Volume adds a third dimension—height. Volume is measured in cubic units rather than square units like area. If your answer is 326 cubic inches, for example, it can also be written 326 inches3 (on the computer, it can be written as 326 inches^3). To help you remember this, you might think of the exponent 3 as referring to a 3-dimensional object. Volume word problems may ask you to find how much a container will hold or the capacity of boxes, rooms, etc.

radius

radius is a line segment that goes from the center of the circle to a point on the circle—in other words, the radius is a line that goes halfway across the circle from or to the center. The radius is half of the diameter.

the perimeter of a square is: Perimeter = 4 * side

the perimeter of a square is: Perimeter = 4 * side