Question

Find the area of a parallelogram if a base and corresponding altitude have the indicated lengths.

Base 1 1/2 feet, altitude 6 inches.

Answer 1

108 square inches

Explanation:

We know that the formula of area of a parallelogram is given by:

A = base × altitude

Since here we have different units for base and altitude, so either we will change the base to inches or the altitude to feet.

Base =
`1(1)/(2) ft = 1.5 ft`

`(1)/(1.5ft) =(12inches)/(x)`

Base (x) = 18 inches

Substituting the values in the above formula to get:

Area of parallelogram = 18 × 6 = 108 square inches

Answer 2

The area of the parallelogram is 108 inches² OR 0.75 foot²

Explanation:

* Lets revise the properties of the parallelogram

- Each two opposite bases are are parallel

- Each two opposite bases are equal in length

- Each two opposite angles are equal in measure

- Each two adjacent angles are supplementary (their sum = 180°)

- Its two diagonals bisect each other

- Each base has an altitude (height) drawn from the opposite

base to it

* Look to the attached figure to more understand

- The area of the parallelogram is the product of the length of one

of its base and the corresponding altitude (height)

∵ Area = B1 × H1 ⇒ OR ⇒ Area = B2 × H2

∵ B1 = 1 1/2 feet

∵ H1 = 6 inches

- The base and the height have different units, so we must

change the unit of one of them to the other

∵ 1 foot = 12 inches

∵ B1 = 1 1/2 = 1.5 feet

∴ B1 = 1.5 × 12 = 18 inches

∴ A = 18 × 6 = 108 inches²

* The area of the parallelogram is 108 inches²

OR

∵ B1 = 1 1/2 = 1.5 feet

∵ H1 = 6 inches

∴ H1 = 6 ÷ 12 = 1/2 = 0.5 foot

∴ A = 1.5 × 0.5 = 0.75 foot²

* The area of the parallelogram is 0.75 foot²