Why it’s base times height
Picture a parallelogram cut out of paper.
Snip the triangle off one end and slide it to the other end. Now you have a rectangle. Nothing was added and nothing was thrown away, so the area didn’t change.
Here’s the key part. The rectangle’s bottom is the base. Its side is the straight-up height. The slanted side disappeared when you made the rectangle, and that’s why it never goes in the formula.
Bottom line: a parallelogram covers the same space as a rectangle with the same base and height.
Example 1: a parking space
A parking space is shaped like a parallelogram. Its base along the curb is 9 feet. The straight-up distance across it is 18 feet. Each slanted side is 20 feet. How much ground does the space cover?
The working
- Write the formula: A = b × h
- Pick the height. It’s 18 feet. The 20 feet is the slanted side, so leave it out.
- Multiply: A = 9 × 18 = 162
- Add square units. Area is always in square units, so it’s 162 square feet.
Answer: 162 square feet
Notice the 20. It’s the biggest number in the question, and it’s the one you don’t use.
Example 2: work backward from the area
Some questions give you the area and ask for a side. It’s the same formula, run backward.
A garden bed shaped like a parallelogram covers 72 square feet. Its base is 12 feet. What is its height?
The working
- Write the formula: A = b × h
- Put in what you know: 72 = 12 × h
- Divide both sides by 12: h = 72 ÷ 12 = 6
- Check it: 12 × 6 = 72. The height is 6 feet.
Answer: 6 feet
3 mistakes that cost points
Mistake 1: multiplying by the slanted side
This is the big one. The slanted side is always longer than the height, so the answer comes out too big. If an answer looks bigger than you expected, check which side you used.
Mistake 2: mixing feet and inches
Change everything to the same unit before you multiply. A base of 2 feet and a height of 8 inches? Use 24 inches times 8 inches. That’s 192 square inches.
Mistake 3: cutting it in half like a triangle
The triangle formula has a ½ in it. This one doesn’t. A parallelogram is two matching triangles put together, so its area is twice a triangle’s.
Practice: 5 new questions
Every set is new. Check each answer as you go, and read the working on any you miss before the next one.
Area of a parallelogram: 5 questions
- Questions
- 5
- Timer
- None
- No calculator
- None
New questions every time you start. Do this set as many times as you like.
- Check each answer as you go and read the working before the next question.
- The formula sheet and calculator sit in the toolbar, as they do on the real test.
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Want more? Practice all of geometry and measurement (25 questions, every skill in the topic), or take the full GED math practice test.
Frequently asked questions
Is the area of a parallelogram length times width?
Only if the width is the straight-up height. Length times width works for a rectangle because its sides already stand straight up. A parallelogram leans, so multiply the base by the height between the two parallel sides. The slanted side stays out of it.
How do you find the area of a parallelogram if you don't know the height?
Find the height first. The slanted side, the height and the distance the top is shifted over make a right triangle. So use the Pythagorean theorem: a slanted side of 10 and a shift of 6 give a height of 8, because 10² − 6² = 64.
What is the area of a rhombus?
A rhombus is a parallelogram with four equal sides, so base times height works. Some books also multiply the two diagonals and divide by 2. The GED formula sheet doesn't list a rhombus, so base times height is the one to know.
Keep going
GED math formula sheet
Every formula on the official sheet with a real-life example, plus the 7 it leaves out.
Geometry and measurement practice
25 GED-style questions on area, volume, circles and more, with the working shown.
Free GED math practice test
The full two hours, timed like the real test, with every answer explained.
Written by
Coach Crissy
Math instructor
Coach Crissy teaches the video lessons behind the BooknBoost GED math course, working through GED-style problems on camera: ratios and proportions, percent and interest, mean, median and mode, slope, and the geometry students meet on test day.