sat suite question viewer

Geometry and Trigonometry / Area and volume Difficulty: Medium

A triangular prism has a height of $8 centimeters left parenthesis cm right parenthesis$ and a volume of $216 cm cubed$ . What is the area, $in {cm}^{2}$ , of the base of the prism? (The volume of a triangular prism is equal to $B h$ , where $B$ is the area of the base and $h$ is the height of the prism.)

Back question 24 of 86 Next

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86

Explanation

The correct answer is $27$ . It's given that a triangular prism has a volume of $216 cubic centimeters left parenthesis cm cubed right parenthesis$ and the volume of a triangular prism is equal to $B h$ , where $B$ is the area of the base and $h$ is the height of the prism. Therefore, $216 equals upper B h$ . It's also given that the triangular prism has a height of $8 cm$ . Therefore, $h equals 8$ . Substituting $8$ for $h$ in the equation $216 equals upper B h$ yields $216 equals upper B left parenthesis 8 right parenthesis$ . Dividing both sides of this equation by $8$ yields $27 equals upper B$ . Therefore, the area, $in {cm}^{2}$ , of the base of the prism is $27$ .