Question

assessment practice

1. the parking space shown at the right has an area of $209\\ \text{ft}^2$. a custom truck has rectangular dimensions of 13.5 ft by 8.5 ft. can the truck fit in the parking space? justify your answer.

the area of the truck is 114.5ft^2
which is less than the area of the
parking space (209ft^2).
406 7-1 find areas of parallelograms and rhombuses

Explanation:

Step1: Find parking space base length

The parking space is a parallelogram with area $A = 209\ \text{ft}^2$ and height $19\ \text{ft}$. Use $A = b \times h$, solve for $b$:
$$b = \frac{A}{h} = \frac{209}{19} = 11\ \text{ft}$$

Step2: Calculate truck's area

Truck is a rectangle with $13.5\ \text{ft} \times 8.5\ \text{ft}$:
$$A_{\text{truck}} = 13.5 \times 8.5 = 114.75\ \text{ft}^2$$

Step3: Compare dimensions

Parking space has dimensions $11\ \text{ft}$ (base) and $19\ \text{ft}$ (side). Truck's longest side is $13.5\ \text{ft}$, which is less than $19\ \text{ft}$; truck's shortest side is $8.5\ \text{ft}$, which is less than $11\ \text{ft}$.

Answer:

Yes, the truck can fit. The parking space has a base length of 11 ft and a side length of 19 ft, which are both larger than the truck's dimensions of 13.5 ft and 8.5 ft (the truck's longest side fits within the 19 ft side, and its shortest side fits within the 11 ft base).