Question

ections: partner a completes the problems in column a . .rer each problem, compare your answers. the two proble your answers do not match, switch problems, work your par the final answer in the middle column.volume rowcolumn aanswer1. a craftsman uses the volume of a gem to set the price. one gem is shaped like a regular triangular pyramid. what is the volume of the gem?5.7 cm6 cm4 cm

Explanation:

Step1: Find base triangle area

The base is a triangle with base $6\ \text{cm}$ and height $4\ \text{cm}$. Area of a triangle is $\frac{1}{2} \times \text{base} \times \text{height}$.
$\text{Base Area} = \frac{1}{2} \times 6 \times 4 = 12\ \text{cm}^2$

Step2: Calculate pyramid volume

Volume of a pyramid is $\frac{1}{3} \times \text{base area} \times \text{height}$. The pyramid height is $5.7\ \text{cm}$.
$\text{Volume} = \frac{1}{3} \times 12 \times 5.7$

Step3: Compute final value

Simplify the expression to get the volume.
$\frac{1}{3} \times 12 \times 5.7 = 4 \times 5.7 = 22.8$

Answer:

$22.8\ \text{cubic centimeters}$