Area of Parallelograms

Area of Parallelograms

by Mrs. Kellany Bennett

Please actually watch the videos! If you don't have headphones or earbuds, read the closed captions. You REALLY ought to have some earbuds for school.

​Area in General

• Area is the space contained inside a 2D shape

• ​We use units like square inches (in²) and square meters (m²)to label area

• ​Finding the area of a rectangle is like counting the squares in an array--find the product of the length and the width.

Multiple Choice

What does area mean?

• the distance around a shape

• half the distance around a shape

• the amount of space outside a shape

• the amount of space inside a shape

Multiple Choice

Find the area of the rectangle.

• 21 in²

• 10 in²

• 20 in²

Multiple Choice

Find the area of the rectangle.

BE CAREFUL: Area is always measured in SQUARE units.

• 11 yards

• 24 yards²

• 22 yards²

• 24 yards

Multiple Choice

Find the area of the square.

• 10 cm²

• 20 cm²

• 25 cm²

​What If It's Not a Rectangle?

• You'd have to hope it has grids and start counting

  • ​​the green squares are wholes

  • ​the yellow parts are almost wholes

  • ​the pink parts are almost halves (count each 2 as 1)

  • ​then you'd add up the 3 numbers you got

  • ​Something like 26 for the total area

​Yeah, no... that takes too long!

• ​Regular shapes have area formulas

• ​Let's work on discovering those formulas!

​Parallelograms

• ​By counting squares, try to estimate the area of this parallelogram...

  • ​Hold on to that guess!

• ​The parallelogram is awfully close to a rectangle and we know a rectangle area formula...

• ​Imagine how we could cut this apart and make a rectangle out of it!

​Parallelograms continued

• ​What if we cut off the triangle from the left?

• ​Now, slide that over to the right

• ​It fits perfectly to the slanted part...

• ​Now it's a rectangle!

• ​A 7 by 6 rectangle has an area of 42 square units.

Multiple Choice

Find the area of the parallelogram by mentally decomposing, then rearranging into a rectangle.

• 6 square units

• 4 square units

• 5 square units

• 10 square units

Multiple Choice

Find the area of the parallelogram by mentally decomposing, then rearranging into a rectangle.

• 12 units²

• 10 units²

• 13 units²

• 6 units

Multiple Choice

Find the area of the parallelogram by mentally decomposing, then rearranging into a rectangle.

• 8 square units

• 10 square units

• 15 square units

• 18 square units

Multiple Choice

Find the area of the parallelogram by mentally decomposing, then rearranging into a rectangle.

• 5 square units

• 24 square units

• 10 square units

• 50 square units

Parallelograms

Parallelograms have a base and a height measurement. The height must have a 90 degree angle relating it to the base measurement, so the slanted sides are different from the height of the shape.

​

​It is important NOT to mix up the height and the slanted length.

Parallelograms

A parallelogram's height can sometimes be shown outside the shape, like in this example. The height is 4, the base is the 5 along the bottom, and the slanted 5 is not needed to calculate area.

Parallelogram Area

To find the are of a parallelogram - you multiply the base times the height. The formula is:

Area = base x height

Multiple Choice

What is the base of this parallelogram ?

• 5 cm

• 35 cm

• 7 cm

• 15 cm

Multiple Choice

If we were finding the area of this parallelogram, which value would we NOT use?

Hint: which is NOT the height or the base?

• 2 m

• 2.5 m

• 1.8 m

Multiple Choice

What is the height of this parallelogram?

• 7 cm

• 5 cm

• 15cm

• 12 cm

Multiple Choice

If you were finding the area of this parallelogram, what two values would you multiply? (In other words, what is the base and height?)

• 7 and 15

• 5 and 15

• 7 and 5

Parallelogram Area

Area = base * height

Area = 6 * 10

Area = 60 square centimeters

​

**Notice: we used 10 as the base and 6 as the height because they meet at a right angle; the slanted side (7) was not used to find the area.

​**Notice: base does not always mean bottom.

​Recap

• ​To find the area of a parallelogram, we simply need to mentally decompose it into a rectangle.

• ​Once we have a rectangle, we can find the area with the formula length times width.

• ​However, since the measurements aren't a length and a width, we'll call them base (length) and height (width).

Parallelogram Area

To find the area of this parallelogram we multiply base * height.

Area = 7 x 4 = 28 square units

​

**Notice we did not use the slanted side (5) to find the area. The base and height must meet at a RIGHT angle.

​IMPORTANT!

• ​If you are given the length of the slanted side of the parallelogram, NEVER use it to find the area!

• ​In this example, the measurement of 6 inches would be helpful for finding the perimeter, but for the AREA we don't need it! Only the height, 5.

• ​Height is often shown with a dotted line and right angle.

Multiple Choice

What does A stand for in the formula

A = bh

• Area

• base

• height

• perimeter

Multiple Choice

What does b stand for in the formula

A = bh

• Area

• base

• height

• perimeter

Multiple Choice

What does h stand for in the formula

A = bh

• Area

• base

• height

• perimeter

Multiple Choice

Find the height of the parallelogram.

• 5 cm

• 7 cm

• 15 cm

• None of these

Multiple Choice

What is the area of this parallelogram?

• 20 square cm

• 25 square cm

• 15 square cm

• 50 square cm

Multiple Choice

What is the area of this parallelogram?

• 75 square in

• 60 square in

• 30 square in

• 50 square in

Multiple Choice

Find the area of this parallelogram

• 12cm²

• 35cm²

• 17.5cm²

• 30cm²

Multiple Choice

Find the area of the parallelogram.

• 20 in²

• 84 in²

• 40 in

• 84 cm²

Multiple Choice

Find the area of this parallelogram

BE CAREFUL--It's kind of turned sideways, but the base and height still meet at a RIGHT angle.

• 70cm²

• 35cm²

• 17cm²

• 70cm

Multiple Choice

Find the area of this parallelogram.

BE CAREFUL--It's kind of turned sideways, but the base and height still meet at a RIGHT angle.

• 110cm²

• 100cm²

• 1100cm²

• 50cm²

Multiple Choice

Find the area of this parallelogram

BE CAREFUL--It's kind of turned sideways, but the base and height still meet at a RIGHT angle.

• 135mm²

• 180mm²

• 108mm²

• 1620mm²

Multiple Choice

Find the area of this parallelogram

BE CAREFUL--The base and height MUST meet at a right angle. This may alter which measurement you see as the base.

• 35m²

• 42m²

• 210m²

• 30m²

Multiple Choice

What is the area of this parallelogram?

• 75 square cm

• 35 square cm

• 15 square cm

• 105 square cm

Open Ended

Explain in your own words how to find the area of a parallelogram.

Don't hit the enter key until you are ready to submit your answer!