SME
Grade 7 Math · Problem type
Prism on a trapezoid
Use this for “A wooden block is a prism on a trapezoid: parallel sides 14 cm and 6 cm, 9 cm apart, 4 cm thick. What is its volume?”
Diagram
Area: 54 cm².
Leaning the shape keeps the base, the height and the area.
h = 5 cm (prism height)
V = 270 cm³ (volume)
This is an example. Type your own values to start a new problem.
B
=
(
a
+
b
)
÷
2
×
t
V
=
B
×
h
Formulas
B
=
(
a
+
b
)
÷
2
×
t
(base
area
=
(long
base
+
short
base)
÷
2
×
trapezoid
height)
54 = (11 + 7) ÷ 2 × 6
V
=
B
×
h
(volume
=
base
area
×
prism
height)
270 = 54 × 5
Assumptions
•
The base is a trapezoid: its area is the average of the two parallel sides × the distance between them.
•
Volume = base area × the prism’s height.
•
All lengths in the same unit; volume in cubic units.
Step-by-step
WE KNOW
a = 11 cm (long base), b = 7 cm (short base), t = 6 cm (trapezoid height), h = 5 cm (prism height)
FIND
base area (B), volume (V)
Step 1 · Find base area (B)
Use B = (a + b) ÷ 2 × t (base area = (long base + short base) ÷ 2 × trapezoid height)
The average of the parallel sides times the distance between them.
B
=
11 + 7
2
×
6
B
=
18
2
×
6
B
=
9
×
6
B
=
54
cm²
Step 2 · Find volume (V)
Use V = B × h (volume = base area × prism height)
Stack the base area up the prism’s height.
V
=
54
×
5
V
=
270
cm³
Check
Put the numbers back in. Both sides should match.
54 = (11 + 7) ÷ 2 × 6 ✓
270 = 54 × 5 ✓
Topic check
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Volume and surface area of prisms
Main lesson
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Use this for “Which solids are prisms?” before using V = Bh.