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Student View

Emma's iPad
besidemath.com/learn

7th Grade Math

What is the volume of this prism?

Trapezoidal Prism
cubic millimeters
Live Scratch Pad
Tri prism:
base = 40 - 32 = 8
V = ½ × 8 × 7 × 15 = 420
Rect prism:
V = 32 × 15 × 7 = 3360
Total = 420 + 3360 =  

🎓 Step-by-Step

✓

Step 1

Break the prism into two simpler sections: a triangular prism and a rectangular prism.

8 7 15

Triangle

+
32 7 15

Rectangle

2

Current Step

Calculate the specific volume of each section.

Triangle V = ½ × base × height × depth
Rectangle V = length × width × depth

Step 3

Add the two calculated volumes together to find the total.

Live Sync Mode

Parent's Phone
Edu GUIDE
E
Emma Smith Live
Grade 7 • Mathematics • Chapter 7. Surface Area and Volume
Parent Access Michael Smith

Live Question Sync

7th Grade Math: Calculating Volume

The student is calculating the volume of a trapezoidal prism given the base dimensions and depth.
Live Sync: Student Scratch Pad
Tri prism:
base = 40 - 32 = 8
V = ½ × 8 × 7 × 15 = 420
Rect prism:
V = 32 × 15 × 7 = 3360
Total = 420 + 3360 =  
💡

Detailed Coaching Guide

Background & Formulas

While a trapezoidal prism's volume can be found using base area multiplied by depth, students commonly struggle. A highly effective alternative is decomposing the shape into two familiar 3D sections:

  • Triangular Prism: Volume = ½ × base × height × depth
  • Rectangular Prism: Volume = length × width × depth

Solution Method Assessment

Emma has successfully decomposed the shape and calculated the two separate sectional volumes! She found 420 for the triangular section and 3360 for the rectangular section.

Crucial Next Step to Coach

"She cracked it! Emma successfully added the volumes together to reach 3780. Applaud her for applying the decomposition method effectively rather than trying to memorize a complex single formula."