Final answer:
To find the area of the parallelogram, multiply the base (12 inches) by the height (8 inches) and divide by 2 to get the area of the triangle, then multiply by 2. The area of the parallelogram is 96 in².
Step-by-step explanation:
The question asks to find the area of a parallelogram using the dimensions provided for a triangle that results from splitting the parallelogram in half.
To calculate the area of the given triangle, we use the formula for the area of a triangle, which is ½ × base × height.
However, we first need to convert the base of the triangle from feet to inches to ensure consistent units since the height is given in inches.
There are 12 inches in 1 foot, so the base of 1 foot is equivalent to 12 inches. The triangle has a base of 12 inches and a height of 8 inches.
Using the area formula for a triangle, we compute the area as follows:
- Area = ½ × base × height
- Area = ½ × 12 in × 8 in
- Area = ½ × 96 in²
- Area = 48 in²
Since this is the area of half of the parallelogram (one triangle), we need to double it to find the full area of the parallelogram:
- Full area of parallelogram = 2 × Area of the triangle
- Full area of parallelogram = 2 × 48 in²
- Full area of parallelogram = 96 in²
Therefore, the area of the parallelogram is 96 square inches.