Question

the composite figure is made up of a triangular prism and a pyramid. the two solids have congruent bases. what is the volume of the composite figure? 715 units³ 2,035 units³ 2,750 units³ 3,465 units³

Explanation:

Step1: Calculate base triangle area

The base is a triangle with base 22 and height 10. Area formula: $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$
$\text{Base Area} = \frac{1}{2} \times 22 \times 10 = 110$ units²

Step2: Find prism volume

Prism volume formula: $\text{Volume} = \text{Base Area} \times \text{height}$
Prism height = 25, so:
$\text{Prism Volume} = 110 \times 25 = 2750$ units³

Step3: Find pyramid volume

Pyramid volume formula: $\text{Volume} = \frac{1}{3} \times \text{Base Area} \times \text{height}$
Pyramid height = 19.5, so:
$\text{Pyramid Volume} = \frac{1}{3} \times 110 \times 19.5 = 715$ units³

Step4: Sum volumes for total

Add prism and pyramid volumes:
$\text{Total Volume} = 2750 + 715$

Answer:

3,465 units³