SME
Grade 7 Math · Problem type
Tent-shaped prism
Use this for “A toy tent is a prism: its end is a triangle with base 16 cm, height 6 cm and two 10 cm sides, and it is 25 cm long.”
Diagram
2 × 48 + 10 × 25 + 16 × 25 + 10 × 25 = 996
Two triangles and three rectangles add to 996 cm².
This is an example. Type your own values to start a new problem.
b
Base of the triangle
example
h
Height of the triangle
example
s
Each 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
=
base
of
the
triangle
×
height
of
the
triangle
÷
2)
48 = 16 × 6 ÷ 2
V
=
B
×
L
(volume
=
area
of
one
end
×
length)
1,200 = 48 × 25
S
=
2
×
B
+
L
×
(
b
+
2
×
s
)
(surface
area
=
2
×
area
of
one
end
+
length
×
(base
of
the
triangle
+
2
×
each
slanted
side))
996 = 2 × 48 + 25 × (16 + 2 × 10)
Assumptions
•
The two ends are the same triangle with two equal slanted sides; each rectangle is one side of the triangle by the length.
•
Volume = the triangle’s area × the length; the triangle’s area is base × height ÷ 2.
•
Surface area = two triangles + the length × the distance around the triangle.
Step-by-step
WE KNOW
b = 16 cm (base of the triangle), h = 6 cm (height of the triangle), s = 10 cm (each slanted side), L = 25 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 = base of the triangle × height of the triangle ÷ 2)
The end is a triangle: half of base times height.
B
=
16
×
6
2
B
=
96
2
B
=
48
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
=
48
×
25
V
=
1,200
cm³
Step 3 · Find surface area (S)
Use S = 2 × B + L × (b + 2 × s) (surface area = 2 × area of one end + length × (base of the triangle + 2 × each slanted side))
Two triangles, and three rectangles: the floor and the two slanted sides.
S
=
2
×
48
+
25
×
(16
+
2
×
10)
S
=
2
×
48
+
25
×
(16
+
20)
S
=
2
×
48
+
25
×
36
S
=
96
+
900
S
=
996
cm²
Check
Put the numbers back in. Both sides should match.
48 = 16 × 6 ÷ 2 ✓
1,200 = 48 × 25 ✓
996 = 2 × 48 + 25 × (16 + 2 × 10) ✓
Topic check
See what you know: 5 questions on this topic
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