Question

independent practice
each of the cards on the left has the same solution as o
cards with matching solutions to complete the sentences
solving for volume, missing side lengths or the area of tr
a determine the volume.
6 units 8 units
5 units
10 units
b calculate the volume of the prism.
14 units 6 units
17 units
c the volume of the
prism is 2,688 cubic
units. what is the value
of the missing side?
8 units 10 units
12 units
x
a triangular prism has a volume of 27.36
cubic units. the prism is 2.88 units tall.
what is the area of the triangular base?

Explanation:

Step1: Calculate Card A volume

First find area of triangular base: $\frac{1}{2} \times 6 \times 8 = 24$ square units.
Volume $V = 24 \times 5 = 120$ cubic units.

Step2: Calculate Card B volume

Find area of triangular base: $\frac{1}{2} \times 14 \times 6 = 42$ square units.
Volume $V = 42 \times 17 = 714$ cubic units.

Step3: Solve Card C missing side

First find area of triangular base: $\frac{1}{2} \times 8 \times 10 = 40$ square units.
Rearrange volume formula: $x = \frac{V}{B} = \frac{2688}{40} = 67.2$ units.

Step4: Solve Card D base area

Rearrange volume formula: $B = \frac{V}{h} = \frac{27.36}{2.88} = 9.5$ square units.

Answer:

Card A: 120 cubic units
Card B: 714 cubic units
Card C: 67.2 units
Card D: 9.5 square units