Question

a horizontal line separates the solid figure into two rectangular prisms. write an expression for the volume of the solid figure. the expression is dropdown with a hand pointing to it (image of a 3d solid with dimensions: 12 ft, 7 ft, 5 ft, 5 ft, 4 ft, 9 ft, 12 ft, 12 ft, 12 ft)

Explanation:

Step1: Identify top prism dimensions

Top prism: length $12$ ft, width $7$ ft, height $5$ ft
Volume of top prism: $V_1 = 12 \times 7 \times 5$

Step2: Identify bottom prism dimensions

Bottom prism: length $12$ ft, width $12$ ft, height $4$ ft
Volume of bottom prism: $V_2 = 12 \times 12 \times 4$

Step3: Total volume expression

Add volumes of both prisms: $V = V_1 + V_2$

Answer:

$12 \times 7 \times 5 + 12 \times 12 \times 4$ (or simplified as $420 + 576$, or combined as $996$ cubic feet, but the factored/expanded expression is the required form)