Question

the figure below is made of two identical triangular prisms. what is the volume of the figure? 100 cubic inches 150 cubic inches 600 cubic inches 300 cubic inches

Explanation:

Step1: Find the base area of the triangular prism

The base of the triangular prism is a triangle. The base of the triangle is \( 5 \) in and the height of the triangle is \( 6 + 6 = 12 \) in. The area of a triangle is \( \frac{1}{2} \times \text{base} \times \text{height} \), so the base area \( B=\frac{1}{2}\times5\times12 = 30 \) square inches.

Step2: Find the volume of one triangular prism

The length (or the distance along the prism) is \( 10 \) in. The volume of a prism is \( V = B\times h \) (where \( h \) is the length of the prism). So the volume of one triangular prism is \( 30\times10 = 300 \) cubic inches. Wait, no, wait. Wait, actually, looking at the figure, maybe the height of the triangle is \( 6 \) and the base is \( 5 \), and the length of the prism is \( 10 \)? Wait, no, let's re - examine. Wait, the two prisms are identical. Wait, maybe the base triangle has base \( 5 \) in, height \( 6 \) in, and the length of the prism is \( 10 \) in. Then the volume of one triangular prism is \( V_1=\frac{1}{2}\times5\times6\times10 \). Let's calculate that: \( \frac{1}{2}\times5\times6 = 15 \), then \( 15\times10 = 150 \) cubic inches.

Step3: Find the volume of the figure (two prisms)

Since the figure is made of two identical triangular prisms, the total volume \( V = 2\times V_1 \). We found \( V_1 = 150 \) cubic inches, so \( V=2\times150 = 300 \) cubic inches? Wait, no, wait. Wait, maybe I made a mistake in step 2. Wait, let's re - calculate the volume of a triangular prism. The formula for the volume of a triangular prism is \( V=\text{Area of base}\times\text{length of the prism} \). The base is a triangle with base \( b = 5 \) in and height \( h_{triangle}=6 \) in (wait, the two 6s: maybe the height of the triangle is 6, and the length of the prism is 10, and there are two prisms. Wait, no, let's look at the figure again. The figure is made of two identical triangular prisms. Let's find the volume of one prism first. The base triangle: base \( = 5 \) in, height \( = 6 \) in (wait, the two 6s: maybe the height of the triangle is 6, and the length of the prism is 10. Then the area of the triangular base is \( \frac{1}{2}\times5\times6=15 \) square inches. The volume of one prism is \( 15\times10 = 150 \) cubic inches. Then two prisms: \( 2\times150 = 300 \) cubic inches. Wait, but let's check again. Wait, maybe the height of the triangle is \( 6 + 6=12 \)? No, the right angle is marked, so the height of the triangle is 6, and the other 6 is maybe part of the other prism? Wait, no, the figure is two identical triangular prisms. So each prism has a triangular base with base 5, height 6, and length 10. So volume of one prism: \( \frac{1}{2}\times5\times6\times10 = 150 \). Two prisms: \( 150\times2 = 300 \).

Answer:

300 cubic inches