Area of Parallelograms

Show your work for each problem.

1.
What is the formula for the area of a parallelogram?
1. a)
2. b)
3. c)
4. d)
Answer:
The area of a parallelogram is base times height: . The second option is addition (not area), the third is perimeter, and the fourth only uses one dimension.
2.
Find the area of a parallelogram with base 6 cm and height 4 cm.
Answer: 24
cm²
3.
Which measurement is the height in a parallelogram?
1. a)The diagonal
2. b)The perpendicular distance from base to opposite side
3. c)The length of the slanted side
4. d)The perimeter
Answer: The perpendicular distance from base to opposite side
The height is always the perpendicular (90°) distance from the base to the opposite parallel side. It's not the slanted side, perimeter, or diagonal.
4.
A parallelogram has base 10 m and height 3 m. What is its area?
Answer: 30
m²
5.
Find the area of a parallelogram with base 7 cm and height 5 cm.
Answer: 35
1. What formula do we use for the area of a parallelogram? A = b × h
2. Substitute the values: A = ? × ? 7 × 5
3. Calculate 7 × 5 35
6.
A parallelogram has sides of 12 cm and 8 cm. The perpendicular height to the 12 cm base is 6 cm. What is the area?
1. a)72 cm²
2. b)48 cm²
3. c)96 cm²
4. d)20 cm²
Answer: 72 cm²
cm². The 8 cm side is not needed for the area calculation.
7.
A parallelogram has an area of 56 cm² and a base of 8 cm. What is the height?
Answer: 7
Using , we rearrange to cm.
8.
Find the base of a parallelogram with area 63 m² and height 9 m.
Answer: 7
1. Write the area formula A = b × h
2. Substitute known values: 63 = b × ? 9
3. Solve for b: b = 63 ÷ 9 7
9.
A parallelogram has base 15 cm and height 8 cm. What is its area?
Answer: 120
cm²
10.
A parallelogram-shaped tile has base 25 cm and height 20 cm. If you need to cover 1 m², how many tiles do you need?
Answer: 20
1. Find the area of one tile in cm²: 25 × 20 = ? 500
2. Convert 1 m² to cm²: 1 m² = ? cm² 10000
3. Divide: 10000 ÷ 500 = ? 20
11.
If you double the height of a parallelogram, what happens to the area?
1. a)The area doubles
2. b)The area is halved
3. c)The area quadruples
4. d)The area stays the same
Answer: The area doubles
If , then doubling h gives . The area doubles.
12.
A parallelogram has base 12.5 cm and height 6.4 cm. What is its area?
Answer: 80
cm²
13.
Two parallelograms have the same area. One has base 16 cm and height 9 cm. The other has base 12 cm. What is the height of the second parallelogram?
Answer: 12
1. Find the area of the first parallelogram: 16 × 9 = ? 144
2. The second parallelogram has the same area. What is it? 144
3. Find height: h = 144 ÷ 12 = ? 12
14.
A parallelogram has base 20 m and one side of 15 m. If the perpendicular height to the base is 12 m, what is the area?
1. a)300 m²
2. b)35 m²
3. c)240 m²
4. d)180 m²
Answer: 240 m²
m². The 15 m side is extra information.
15.
A garden in the shape of a parallelogram has an area of 180 m². If the base is 15 m, what is the height? Then, if fencing costs 8 euros per meter and you need to fence two sides of height, how much does the fencing cost?
Answer: 192
1. Find the height: h = 180 ÷ 15 = ? 12
2. Calculate total fencing needed: 2 × height = 2 × 12 = ? 24
3. Calculate cost: 24 × 8 = ? 192
16.
A parallelogram-shaped field has an area of 2400 m². If a farmer wants to divide it into 6 equal parallelogram plots, what is the area of each plot?
Answer: 400
Each plot: m²
17.
True or False: A rectangle is a special type of parallelogram.
1. a)True
2. b)Only if it's a square
3. c)False
4. d)Only sometimes
Answer: True
True! A rectangle has two pairs of parallel sides, just like a parallelogram. It's a parallelogram where all angles are 90°.
18.
A sail on a boat is shaped like a parallelogram. The base is 3.5 m and the height is 4 m. What is the sail's area?
Answer: 14
1. Write the formula for area A = b × h
2. Substitute: A = 3.5 × ? 4
3. Calculate: 3.5 × 4 = ? 14