To find the volume of a triangular prism, you use this formula:
Volume = Area of the Triangle Base × Length of the Prism
1.
Find the Area of the Triangle: The formula for the area of a triangle is $\frac{1}{2} \times \text{base} \times \text{height}$. Look for the side with the right-angle symbol (the little square) to identify the base and height of the triangle face.
2.
Multiply by the Length: Take that area and multiply it by the length of the prism (the distance connecting the front triangle to the back triangle).
Here are the step-by-step solutions for each problem:
1)
*
Triangle Base: 10 in,
Height: 14 in.
* Area = $0.5 \times 10 \times 14 = 70$ sq in.
*
Length: 19 in.
* Volume = $70 \times 19 = 1330$
2)
*
Triangle Base: 18 ft,
Height: 17 ft.
* Area = $0.5 \times 18 \times 17 = 153$ sq ft.
*
Length: 5 ft.
* Volume = $153 \times 5 = 765$
3)
*
Triangle Base: 11 yd,
Height: 6 yd.
* Area = $0.5 \times 11 \times 6 = 33$ sq yd.
*
Length: 8 yd.
* Volume = $33 \times 8 = 264$
4)
*
Triangle Base: 7 ft,
Height: 5 ft.
* Area = $0.5 \times 7 \times 5 = 17.5$ sq ft.
*
Length: 9 ft.
* Volume = $17.5 \times 9 = 157.5$
5)
*
Triangle Base: 10 yd,
Height: 7 yd.
* Area = $0.5 \times 10 \times 7 = 35$ sq yd.
*
Length: 4 yd.
* Volume = $35 \times 4 = 140$
6)
*
Triangle Base: 5 in,
Height: 9 in.
* Area = $0.5 \times 5 \times 9 = 22.5$ sq in.
*
Length: 11 in.
* Volume = $22.5 \times 11 = 247.5$
7)
*
Triangle Base: 19 yd,
Height: 8 yd.
* Area = $0.5 \times 19 \times 8 = 76$ sq yd.
*
Length: 4 yd.
* Volume = $76 \times 4 = 304$
8)
*
Triangle Base: 11 in,
Height: 12 in.
* Area = $0.5 \times 11 \times 12 = 66$ sq in.
*
Length: 14 in.
* Volume = $66 \times 14 = 924$
9)
*
Triangle Base: 13 ft,
Height: 16 ft.
* Area = $0.5 \times 13 \times 16 = 104$ sq ft.
*
Length: 20 ft.
* Volume = $104 \times 20 = 2080$
Final Answer:
1) 1330 in³
2) 765 ft³
3) 264 yd³
4) 157.5 ft³
5) 140 yd³
6) 247.5 in³
7) 304 yd³
8) 924 in³
9) 2080 ft³
Parent Tip: Review the logic above to help your child master the concept of volume prisms worksheet.
