Lesson 5.1Area of Rhombuses
Start hereWords, worked example, and sentence starters
Learning target I can find the area of a parallelogram using base × height.
Start hereWords for this lesson
Read each word before you begin. Say it out loud.
| Word | What it means | Example |
|---|---|---|
| Slanted sideSpanish: Lado inclinado | A side that leans instead of going straight up and down. It is not the perpendicular height. | In a leaning parallelogram, use the dashed 90° height—not the slanted side—in A = b × h. |
| ParallelogramSpanish: Paralelogramo | A four-sided shape with two pairs of parallel sides. | Think of a leaning door — the top and bottom are parallel, and the two sides are parallel, like a slanted rectangle |
| ParallelSpanish: Paralelas | Two lines or sides that stay the same distance apart and never meet. | The top and bottom of a parallelogram never get closer together — matching arrowheads (›) mark one parallel pair, double arrowheads (››) mark the other. |
| BaseSpanish: Base | Any side of a parallelogram can be the base. Once you pick a base, the height must be measured perpendicular (at a 90° angle) to it. | Any side can be the base: choose the 10 cm side and b = 10 cm, then draw the height at 90° to that side in A = b × h |
| HeightSpanish: Altura | The straight-up distance from the base to the top. | A dashed vertical line from the top side straight down to the base, forming a 90° angle — NOT the slanted side |
| PerpendicularSpanish: Perpendicular | Two lines that meet to make a square corner (90 degrees). | diagonals meet at 90° |
How it worksWorked examplefinding the area of a rhombus
These numbers are not on your problems. The steps are. Follow them with your own numbers.
A rhombus has a side length of 13 cm and a perpendicular height of 8 cm. Find the area.
- A rhombus IS a parallelogram, so use A = b × h.
- Any side can be the base. b = 13 cm
- Use the perpendicular height, never a slanted side. h = 8 cm
- Multiply and label square units. 13 × 8 = 104
Answer: The area of the rhombus is 104 square centimeters (104 cm²).
Now you trySame steps, your turn
The steps are the same as the worked example. The numbers are yours. Do the work.
A rhombus has a side length of 11 cm and a perpendicular height of 6 cm. Find the area.
- Which formula fits a rhombus? A = ×
- Base = cm
- Perpendicular height = cm
- Multiply. × = Units:
Say it and write itSentence starters
Finish each sentence out loud with a partner. Then use them in your writing.
- A rhombus is a parallelogram because .
- I used as the base and as the height.
- Area = × = square units.
- When only the diagonals are given, I first .
Word bank rhombusparallelogramcongruentdiagonalhalfperpendicularbaseheightarearectanglerearrangesquare units
Watch outA common mistake
The most common mistake in Area of Parallelograms is multiplying the base by the slanted side instead of the perpendicular height. For a parallelogram with a base of 16 ft, a perpendicular height of 9 ft, and a slanted side of 11 ft, students compute 16 × 11 = 176 square feet instead of the correct 16 × 9 = 144 square feet. The height must be the straight-up (perpendicular) distance between the base and its opposite side, not the length of the slanted side, even though the slanted side is often the number that 'looks' like it belongs in the formula.
Lesson 5.1Area of Rhombuses
Apply Day · Version ASupported practice
Learning target I can find the area of a parallelogram using base × height.
-
1Complete each step, then write the final answer.
A parallelogram has a base of 6 m and a height of 3 m. Find its area.
Show your workHint Multiply the base by the height.
Final answer: -
2Complete each step, then write the final answer.
A parallelogram has a base of 8 in, a height of 2 in and a slanted side of 3 in. Find its area.
Show your workHint Use the height, not the slanted side.
Final answer: -
3Complete each step, then write the final answer.
A rug is shaped like a parallelogram. Its base is 7 feet and its height is 5 feet. What is its area?
Show your workHint Multiply the base by the height.
Final answer:
Lesson 5.1Area of Rhombuses
Apply Day · Version BCore practice
Learning target I can find the area of a parallelogram using base × height.
-
1Complete each step, then write the final answer.
Leo finds the area of a parallelogram. The base is 11 cm, the slanted side is 7 cm and the height is 5 cm. He writes 11 × 7 = 77. What is the correct area?
Show your workFinal answer: -
2Complete each step, then write the final answer.
A parallelogram has an area of 91 square centimeters. Its height is 7 cm. How long is its base?
Show your workFinal answer: -
3Complete each step, then write the final answer.
A parallelogram has a base of 13 m and a height of 4 m. Find its area.
Show your workFinal answer:
Lesson 5.1Area of Rhombuses
Apply Day · ChallengeExtension
Learning target I can find the area of a parallelogram using base × height.
-
1Circle the letter of the best answer. Show how you know.
A parallelogram-shaped patio has a base of 16 feet and a perpendicular height of 9 feet. What is its area?
- A25 square feet
- B50 square feet
- C72 square feet
- D144 square feet
FormulaPut the numbers inWork it outAnswer with its unit -
2Complete each step, then write the final answer.
Ana multiplies the two side lengths of a parallelogram, 9 cm and 6 cm, and gets 54 square centimeters. The height to the 9 cm side is 4 cm. What is the real area?
Show your workFinal answer: -
3Complete each step, then write the final answer.
A parallelogram has an area of 84 square meters and a base of 12 meters. What is its height?
Show your workFinal answer: