Question

11.3.ip - 13
a horizontal line separates the solid figure into two rectangular prisms. write an expression for the volume of the solid figure.
the expression is
(image: a 3d solid figure with dimensions: 12 ft (length), 9 ft (height), 12 ft (width) for the base; a top part with 7 ft (length), 5 ft (height), 5 ft (width); and a lower extension with 12 ft (length), 4 ft (height), 5 ft (width))

Explanation:

Step1: Identify top prism dimensions

The top rectangular prism has length $12$ ft, width $7$ ft, height $9-4=5$ ft.
Volume of top prism: $V_1 = 12 \times 7 \times 5$

Step2: Identify bottom prism dimensions

The bottom rectangular prism has length $12$ ft, width $7+5=12$ ft, height $4$ ft.
Volume of bottom prism: $V_2 = 12 \times 12 \times 4$

Step3: Total volume expression

Add the volumes of the two prisms.
Total volume: $V = V_1 + V_2 = 12 \times 7 \times 5 + 12 \times 12 \times 4$

Answer:

$12 \times 7 \times 5 + 12 \times 12 \times 4$ (or simplified to $420 + 576 = 996$ cubic feet, but the factored expression is also acceptable: $12(35 + 48) = 12 \times 83$)