Let’s solve each problem one by one. We’re finding the
volume of a triangular prism.
The formula for volume of a triangular prism is:
>
Volume = (Area of triangular base) × (Length of prism)
And area of a triangle =
½ × base × height
So overall:
>
Volume = ½ × base × height × length
We’ll use this for each shape. Let’s go step by step.
---
Problem 1:
Triangle base = 3, triangle height = 4, prism length = 6
Volume = ½ × 3 × 4 × 6
= ½ × 12 × 6
= 6 × 6
=
36
---
Problem 2:
Triangle base = 5, triangle height = 8, prism length = 7
Volume = ½ × 5 × 8 × 7
= ½ × 40 × 7
= 20 × 7
=
140
---
Problem 3:
Triangle base = 6, triangle height = 4, prism length = 9
Volume = ½ × 6 × 4 × 9
= ½ × 24 × 9
= 12 × 9
=
108
---
Problem 4:
This one looks like a house-shaped prism — but it’s still a triangular prism on top of a rectangular part? Wait — no! Looking carefully, the shaded triangle is the base, and the “length” is going into the page.
Actually, in all these diagrams, the gray triangle is the cross-section (the base), and the dimension labeled along the side is the length of the prism.
In Problem 4: Triangle base = 6, triangle height = 4, prism length = 10
Wait — let me check the diagram again mentally. The triangle has base 6 and height 4, and the prism extends 10 units long.
So same formula:
Volume = ½ × 6 × 4 × 10
= ½ × 24 × 10
= 12 × 10
=
120
---
Problem 5:
Triangle base = 8, triangle height = 5, prism length = 12
Volume = ½ × 8 × 5 × 12
= ½ × 40 × 12
= 20 × 12
=
240
---
Problem 6:
Triangle base = 4, triangle height = 9, prism length = 7
Volume = ½ × 4 × 9 × 7
= ½ × 36 × 7
= 18 × 7
=
126
---
Problem 7:
Triangle base = 5, triangle height = 6, prism length = 10
Volume = ½ × 5 × 6 × 10
= ½ × 30 × 10
= 15 × 10
=
150
---
Problem 8:
Triangle base = 7, triangle height = 4, prism length = 11
Volume = ½ × 7 × 4 × 11
= ½ × 28 × 11
= 14 × 11
=
154
---
Problem 9:
Triangle base = 10, triangle height = 6, prism length = 8
Volume = ½ × 10 × 6 × 8
= ½ × 60 × 8
= 30 × 8
=
240
---
Now let’s list them in order:
1. 36
2. 140
3. 108
4. 120
5. 240
6. 126
7. 150
8. 154
9. 240
Double-checking a couple to be sure:
Problem 2: ½×5×8×7 → 20×7=140 ✔️
Problem 5: ½×8×5×12 → 20×12=240 ✔️
Problem 9: ½×10×6×8 → 30×8=240 ✔️
All look correct.
Final Answer:
1. 36
2. 140
3. 108
4. 120
5. 240
6. 126
7. 150
8. 154
9. 240
Parent Tip: Review the logic above to help your child master the concept of volume of a triangular prism worksheet.
