Geometry: Area and Perimeter (Middle School)
Solve real-world problems with rectangles, triangles, parallelograms, trapezoids, and composite figures
Geometry: Area and Perimeter (Middle School)
Solve real-world problems with rectangles, triangles, parallelograms, trapezoids, and composite figures
Geometry - Grade 6-8
- 1
A rectangle is 12 centimeters long and 7 centimeters wide. Find its area and perimeter.
The area is 84 square centimeters because 12 × 7 = 84. The perimeter is 38 centimeters because 2(12 + 7) = 38. - 2
A square garden has a side length of 9 feet. Find the area and perimeter of the garden.
A square has four equal sides.
The area is 81 square feet because 9 × 9 = 81. The perimeter is 36 feet because 4 × 9 = 36. - 3
A triangle has a base of 14 inches and a height of 6 inches. Find the area of the triangle.
Use A = 1/2bh.
The area is 42 square inches because the area of a triangle is 1/2 × base × height, so 1/2 × 14 × 6 = 42. - 4
A parallelogram has a base of 10 meters and a height of 8 meters. Find its area.
The area is 80 square meters because the area of a parallelogram is base × height, so 10 × 8 = 80. - 5
A trapezoid has bases of 16 centimeters and 10 centimeters. Its height is 5 centimeters. Find the area.
Add the two bases first, then multiply by the height and divide by 2.
The area is 65 square centimeters because A = 1/2(b1 + b2)h, so 1/2(16 + 10)5 = 65. - 6
A rectangular classroom floor is 24 feet long and 18 feet wide. Carpet costs $3 per square foot. How much will it cost to carpet the whole floor?
The floor area is 432 square feet because 24 × 18 = 432. The carpet will cost $1,296 because 432 × 3 = 1,296. - 7
A rectangular picture frame measures 20 inches by 15 inches. What is the perimeter of the frame?
Perimeter is the distance around the outside of a shape.
The perimeter is 70 inches because 2(20 + 15) = 70. - 8
Find the area of an L-shaped figure made from two rectangles. The first rectangle is 8 feet by 4 feet. The second rectangle is 3 feet by 6 feet. The rectangles do not overlap.
Break the figure into two rectangles and add their areas.
The total area is 50 square feet because the first rectangle has area 8 × 4 = 32 and the second rectangle has area 3 × 6 = 18, and 32 + 18 = 50. - 9
A rectangle has an area of 96 square centimeters and a width of 8 centimeters. What is its length?
The length is 12 centimeters because area = length × width, and 96 ÷ 8 = 12. - 10
A square has a perimeter of 52 meters. What is the length of one side, and what is the area of the square?
Divide the perimeter by 4 to find one side of a square.
One side is 13 meters because 52 ÷ 4 = 13. The area is 169 square meters because 13 × 13 = 169. - 11
A triangular flag has side lengths of 9 inches, 12 inches, and 15 inches. What is the perimeter of the flag?
The perimeter is 36 inches because 9 + 12 + 15 = 36. - 12
A park is shaped like a rectangle with a length of 60 yards and a width of 35 yards. A fence will be placed around the park. How many yards of fencing are needed?
Fencing goes around the outside, so find the perimeter.
The park needs 190 yards of fencing because the perimeter is 2(60 + 35) = 190. - 13
A composite shape is made by placing a rectangle and a triangle together. The rectangle is 10 inches long and 6 inches wide. The triangle has a base of 10 inches and a height of 4 inches. Find the total area.
The rectangle area is 60 square inches because 10 × 6 = 60. The triangle area is 20 square inches because 1/2 × 10 × 4 = 20. The total area is 80 square inches. - 14
A regular hexagon has side lengths of 7 centimeters. What is its perimeter?
A regular polygon has all side lengths equal.
The perimeter is 42 centimeters because a hexagon has 6 sides and 6 × 7 = 42. - 15
A student says that a rectangle with an area of 48 square units must have a perimeter of 28 units. Give one example that proves the student is not always correct.
Look for different factor pairs of 48.
One example is a rectangle with side lengths 6 units and 8 units. Its area is 48 square units, but its perimeter is 28 units. To prove the statement is not always correct, another example is 4 units by 12 units, which also has area 48 square units but has perimeter 32 units.