Volume of a Triangular Prism Worksheets | Triangular prism ... - Free Printable

To solve the problem of finding the volume of each triangular prism, we need to use the formula for the volume of a triangular prism:

\[
\text{Volume} = \text{Base Area} \times \text{Height}
\]

The base area of a triangular prism is the area of the triangular base, which can be calculated using the formula for the area of a triangle:

\[
\text{Base Area} = \frac{1}{2} \times \text{base} \times \text{height of the triangle}
\]

Let's solve each problem step by step.

---

Problem 1:

- Dimensions: Base of triangle = 10 in, Height of triangle = 14 in, Length of prism = 19 in
- Base Area:
\[
\text{Base Area} = \frac{1}{2} \times 10 \times 14 = 70 \text{ in}^2
\]
- Volume:
\[
\text{Volume} = \text{Base Area} \times \text{Length} = 70 \times 19 = 1330 \text{ in}^3
\]

Answer: \( \boxed{1330} \)

---

Problem 2:

- Dimensions: Base of triangle = 5 ft, Height of triangle = 17 ft, Length of prism = 18 ft
- Base Area:
\[
\text{Base Area} = \frac{1}{2} \times 5 \times 17 = 42.5 \text{ ft}^2
\]
- Volume:
\[
\text{Volume} = \text{Base Area} \times \text{Length} = 42.5 \times 18 = 765 \text{ ft}^3
\]

Answer: \( \boxed{765} \)

---

Problem 3:

- Dimensions: Base of triangle = 9 yd, Height of triangle = 6 yd, Length of prism = 11 yd
- Base Area:
\[
\text{Base Area} = \frac{1}{2} \times 9 \times 6 = 27 \text{ yd}^2
\]
- Volume:
\[
\text{Volume} = \text{Base Area} \times \text{Length} = 27 \times 11 = 297 \text{ yd}^3
\]

Answer: \( \boxed{297} \)

---

Problem 4:

- Dimensions: Base of triangle = 7 ft, Height of triangle = 5 ft, Length of prism = 8 ft
- Base Area:
\[
\text{Base Area} = \frac{1}{2} \times 7 \times 5 = 17.5 \text{ ft}^2
\]
- Volume:
\[
\text{Volume} = \text{Base Area} \times \text{Length} = 17.5 \times 8 = 140 \text{ ft}^3
\]

Answer: \( \boxed{140} \)

---

Problem 5:

- Dimensions: Base of triangle = 10 yd, Height of triangle = 7 yd, Length of prism = 12 yd
- Base Area:
\[
\text{Base Area} = \frac{1}{2} \times 10 \times 7 = 35 \text{ yd}^2
\]
- Volume:
\[
\text{Volume} = \text{Base Area} \times \text{Length} = 35 \times 12 = 420 \text{ yd}^3
\]

Answer: \( \boxed{420} \)

---

Problem 6:

- Dimensions: Base of triangle = 5 in, Height of triangle = 8 in, Length of prism = 11 in
- Base Area:
\[
\text{Base Area} = \frac{1}{2} \times 5 \times 8 = 20 \text{ in}^2
\]
- Volume:
\[
\text{Volume} = \text{Base Area} \times \text{Length} = 20 \times 11 = 220 \text{ in}^3
\]

Answer: \( \boxed{220} \)

---

Problem 7:

- Dimensions: Base of triangle = 19 yd, Height of triangle = 10 yd, Length of prism = 4 yd
- Base Area:
\[
\text{Base Area} = \frac{1}{2} \times 19 \times 10 = 95 \text{ yd}^2
\]
- Volume:
\[
\text{Volume} = \text{Base Area} \times \text{Length} = 95 \times 4 = 380 \text{ yd}^3
\]

Answer: \( \boxed{380} \)

---

Problem 8:

- Dimensions: Base of triangle = 14 in, Height of triangle = 12 in, Length of prism = 11 in
- Base Area:
\[
\text{Base Area} = \frac{1}{2} \times 14 \times 12 = 84 \text{ in}^2
\]
- Volume:
\[
\text{Volume} = \text{Base Area} \times \text{Length} = 84 \times 11 = 924 \text{ in}^3
\]

Answer: \( \boxed{924} \)

---

Problem 9:

- Dimensions: Base of triangle = 36 ft, Height of triangle = 40 ft, Length of prism = 30 ft
- Base Area:
\[
\text{Base Area} = \frac{1}{2} \times 36 \times 40 = 720 \text{ ft}^2
\]
- Volume:
\[
\text{Volume} = \text{Base Area} \times \text{Length} = 720 \times 30 = 21600 \text{ ft}^3
\]

Answer: \( \boxed{21600} \)

---

Final Answers:

1. \( \boxed{1330} \)
2. \( \boxed{765} \)
3. \( \boxed{297} \)
4. \( \boxed{140} \)
5. \( \boxed{420} \)
6. \( \boxed{220} \)
7. \( \boxed{380} \)
8. \( \boxed{924} \)
9. \( \boxed{21600} \)