SME
Grade 6 Math · Problem type
Surface area of triangular prisms
Use this for “Find the surface area of the triangular prism from its net.”
Diagram
2 × 24 + 8 × 10 + 6 × 10 + 10 × 10 = 288
Two triangles and three rectangles add to 288.
This is an example. Type your own values to start a new problem.
Triangle base
example
Triangle height
example
Third side
example
Prism length
example
Area of one triangle
worked out (not typed)
Area of the three rectangles
worked out (not typed)
Surface area
worked out (not typed)
Formulas
1
2
×
6
×
8
=
24
Half of base × height = area of one triangle
(6 + 8 + 10) × 10 = 240
(Base + height + third side) × length = area of the three rectangles
2 × 24 + 240 = 288
2 × area of one triangle + area of the three rectangles = surface area
Assumptions
•
The net is 2 matching triangles and 3 rectangles, one on each side of the triangle.
•
The three sides of the triangle are given on the net. The base and the height meet at a square corner.
•
The rectangles are all as long as the prism. Their widths are the three sides of the triangle.
Step-by-step
WE KNOW
Triangle base: 6 cm
Triangle height: 8 cm
Third side: 10 cm
Prism length: 10 cm
FIND
area of one triangle, area of the three rectangles, surface area
Step 1 · Find area of one triangle
1
2
×
6
×
8
=
?
Half of base × height = area of one triangle
Each end is a triangle: half of base × height.
Area of one triangle = 24 cm²
Step 2 · Find area of the three rectangles
(6 + 8 + 10) × 10 = ?
(Base + height + third side) × length = area of the three rectangles
The three rectangles side by side make one rectangle: the triangle’s perimeter by the prism’s length.
6 + 8 + 10 = 24
24 × 10 = 240
Area of the three rectangles = 240 cm²
Step 3 · Find surface area
2 × 24 + 240 = ?
2 × area of one triangle + area of the three rectangles = surface area
Add the two triangle ends and the three rectangles.
2 × 24 = 48
48 + 240 = 288
Surface area = 288 cm²
Check
Put the numbers back in. Both sides should match.
1
2
×
6
×
8
=
24
✓
(6 + 8 + 10) × 10 = 240 ✓
2 × 24 + 240 = 288 ✓
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