SME
Grade 7 Math · Problem type
Triangular prism
Use this for “A prism stands on a right triangle with legs 9 and 12 and slanted side 15, and is 20 long. Find its volume and surface area.”
Diagram
2 × 150 + 15 × 8 + 20 × 8 + 25 × 8 = 780
Two triangles and three rectangles add to 780 cm².
This is an example. Type your own values to start a new problem.
b
First leg
example
h
Second leg
example
s
Slanted side
example
L
Length
example
B
Area of one end
worked out (not typed)
V
Volume
worked out (not typed)
S
Surface area
worked out (not typed)
Formulas
B
=
b
×
h
÷
2
(area
of
one
end
=
first
leg
×
second
leg
÷
2)
150 = 20 × 15 ÷ 2
V
=
B
×
L
(volume
=
area
of
one
end
×
length)
1,200 = 150 × 8
S
=
2
×
B
+
L
×
(
b
+
h
+
s
)
(surface
area
=
2
×
area
of
one
end
+
length
×
(first
leg
+
second
leg
+
slanted
side))
780 = 2 × 150 + 8 × (20 + 15 + 25)
Assumptions
•
The two ends are the same right triangle; each rectangle is one side of the triangle by the length.
•
Volume = the triangle’s area × the length.
•
Surface area = two triangles + the length × the distance around the triangle.
Step-by-step
WE KNOW
b = 20 cm (first leg), h = 15 cm (second leg), s = 25 cm (slanted side), L = 8 cm (length)
FIND
area of one end (B), volume (V), surface area (S)
Step 1 · Find area of one end (B)
Use B = b × h ÷ 2 (area of one end = first leg × second leg ÷ 2)
The end is a right triangle: half of leg times leg.
B
=
20
×
15
2
B
=
300
2
B
=
150
cm²
Step 2 · Find volume (V)
Use V = B × L (volume = area of one end × length)
Stack
the
end’
s
area
along
the
length.
V
=
150
×
8
V
=
1,200
cm³
Step 3 · Find surface area (S)
Use S = 2 × B + L × (b + h + s) (surface area = 2 × area of one end + length × (first leg + second leg + slanted side))
Two triangles, and three rectangles: the length times the distance around the triangle.
S
=
2
×
150
+
8
×
(20
+
15
+
25)
S
=
2
×
150
+
8
×
(35
+
25)
S
=
2
×
150
+
8
×
60
S
=
300
+
480
S
=
780
cm²
Check
Put the numbers back in. Both sides should match.
150 = 20 × 15 ÷ 2 ✓
1,200 = 150 × 8 ✓
780 = 2 × 150 + 8 × (20 + 15 + 25) ✓
Topic check
See what you know: 5 questions on this topic
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Volume and surface area of prisms
Main lesson
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