💡 The Big Picture
A triangular prism has 5 faces: 2 triangular ends (bases) and 3 rectangular sides. The surface area is the sum of all 5 face areas. The GED problem gives you the total SA, the area of each triangle, and one dimension — then asks you to find the height (length) of the prism using algebra!
When the triangular bases are equilateral (all 3 sides equal), all 3 rectangular faces have the same dimensions.
This simplifies the formula: instead of adding 3 different rectangles, you multiply one rectangle's area by 3!
• Bases = equilateral triangles (all sides = 25 mm)
• Each triangular face area = 271 mm²
• Base edge of each rectangle = 25 mm
• Height (length) of prism = h (unknown)
Two identical triangular bases.
Area of each = 271 mm²
Total = 2 × 271 = 542 mm²
Three identical rectangular faces.
Each = 25 mm × h mm
Total = 3 × 25 × h = 75h
SA = 2(A_tri) + 3(b × h)
For Dr. Evers' prism:
4,292 = 2(271) + 3(25 × h)
4,292 = 542 + 75h
→ Solve for h!
| Prism Type | Formula |
|---|---|
| Equilateral triangle bases | SA = 2(A_tri) + 3(b × h) |
| General triangle bases | SA = 2(A_tri) + (a+b+c)(h) |
| General form | SA = 2(base area) + perimeter(h) |
SA = 2(A_tri) + 3(b × h)
4,292 = 2(271) + 3(25)(h)
4,292 − 2(271) = 3(25)(h)
h = [4,292 − 2(271)] / 3(25)
Denominator: 3(25) = 75
h = 3,750 ÷ 75 = 50 mm
| Choice | What it computes | Correct? |
|---|---|---|
| 4292 / 3(25) | Divides total SA by rectangle area — ignores triangular faces ❌ | ❌ Wrong |
| 4292 / 271 | Divides by triangle area — gives # of triangle areas, not h ❌ | ❌ Wrong |
| (4292 − 271) / 25 | Subtracts only 1 triangle, divides by only 1 side — missing factors ❌ | ❌ Wrong |
| (4292 − 2(271)) / 3(25) | Subtracts BOTH triangles, divides by area of 3 rectangles ✅ | ✅ CORRECT |
The SA formula has h "hidden" inside: SA = 2(A_tri) + 3(b)(h)
Step 1: Subtract the triangular faces from SA (removes the + part)
Step 2: Divide by 3(b) (removes the multiplication)
4,292 = 2(271) + 3(25)(h)
2 × 271 = 542
4,292 = 542 + 75h
4,292 − 542 = 3,750
3,750 = 75h
h = 3,750 ÷ 75
h = 50 mm
= 542 + 3(1,250)
= 542 + 3,750
= 4,292 mm² ✅
The prism has 2 triangular bases. The GED problem says each triangular face = 271 mm². So the two triangles together = 2 × 271 = 542 mm². You must subtract both from the total SA before dividing!
2 triangular bases + 3 rectangular sides = 5 faces. For equilateral bases, all 3 rectangles are identical → multiply one rectangle by 3.
The GED gives area of ONE triangle, but the prism has TWO. Always multiply by 2 before subtracting from total SA!
The prism diagram shows h as the length of the rectangular sides (how "deep" the prism is). Don't confuse this with the height of the triangular base!
The GED problem asks "which expression CAN BE USED to find h?" — choose the algebraically correct rearrangement without calculating the final answer.
| Goal | Formula |
|---|---|
| Find SA | SA = 2(A_tri) + 3(b × h) |
| Find h (length) | h = (SA − 2·A_tri) / 3(b) |
| GED Problem | h = (4292 − 2·271) / 3(25) |