Neft Teacher · Learn It

Unit 5 · Standard 6.GR.1

Determine the Area of Parallelograms and Rhombuses

Lesson 5-1 · Learn It — how the math works

Why we're learning this

Your architecture firm is designing a parallelogram-shaped patio for a client's backyard. The client needs to know how many square feet of pavers to order. The patio has a base of 14 feet and a height of 9 feet.

✱ Math Workbench

Learn It

How do we find the area of a parallelogram?

A parallelogram is a four-sided shape with two pairs of parallel sides, like a leaning rectangle. Its area is how much flat space is inside it.

Picture itSee what the math looks like before you read about it

The Dockland building in Hamburg, Germany, is built in the shape of a parallelogram leaning over the water.
Where you see this in real lifeThe Dockland building in Hamburg, Germany, is built in the shape of a parallelogram leaning over the water.

Watch me solve itI do — read one step at a time

The problem looks like this
A parallelogram with a base of 14 feet and a perpendicular height of 9 feet. The height is drawn straight up from the base, not along the slanted side. base = 14 feet height = 9 feet The slanted side isNOT the height.
  1. I have a with a of 14 feet and a of 9 feet.
  2. I write the :A = base × height
  3. I put in the numbers:A = 14 × 9
  4. I multiply:14 × 9 = 126
  5. So the is 126 square feet. I used the of 9, not the .

Watch out — mistakes students make here

  • Area of a parallelogram is base × height, not adding sides.
  • 34 is 2 × (10 + 7) — that adds the sides like a perimeter. Area multiplies base × height.
  • Is the height half of 54?

Try it with meWe do — you answer first, then check

Same steps, new numbers.

  1. Now a smaller :base = 5 cm, height = 4 cm
  2. What is the ?
    Check this step
    A = base × height
  3. What do we put in?
    Check this step
    A = 5 × 4
  4. What is 5 × 4?5 × 4
    Check this step
    Yes, 20, so the is 20 square centimeters.

On your ownYou do — solve this one by yourself

Before you start, remember:

  • Remember: multiply the by the , and always use the height.

Solve: What is the of a with 10 cm and 7 cm?

My answer

Stuck? Open one hint at a time.

Hint 1

You know both the base (10 cm) and the height (7 cm) — this is a direct use of the parallelogram area formula.

Hint 2

Area of a parallelogram is A = base × height. Adding the two numbers gives perimeter-style thinking, not area.

Hint 3

Set up A = 10 × 7 and multiply. Label your result in square centimeters.

Check my answer
✅ Answer: 70 sq cm
A = b × h = 10 × 7 = 70 square centimeters.

Turn & TalkSay it out loud with a partner

Look at the patio blueprint with a of 14 feet and a of 9 feet. Why do we use the height (9 ft) and not the to find the ?

Try starting with:

  • We use the height because it is ___ to the base.Usamos la altura porque es ___ a la base.
  • The slanted side is not the height because ___.El lado inclinado no es la altura porque ___.
Use these wordsbaseheightareaparallelogramformula