💡 What You Will Learn
The area of a triangle formula A = ½ × b × h is on the GED formula sheet. But many problems give you the area and one dimension and ask you to find the other — requiring you to solve the formula backwards. This lesson covers both directions!
A triangle fits exactly inside a rectangle of the same base and height. Cut that rectangle diagonally → two equal triangles. So triangle area = ½ × rectangle area.
A = (b × h) ÷ 2
A = bh/2
All three mean the same thing — multiply base by height, then divide by 2.
This formula is provided on the GED exam. You don't need to memorize it — but you must know how to use it and rearrange it to solve for the missing value!
Base (b): Any side of the triangle can be chosen as the base — usually the bottom side.
Height (h): The perpendicular distance from the base to the opposite vertex. It is NOT necessarily a side of the triangle — it can be drawn inside or outside the triangle and is shown with a dashed line and a small square corner (□).
In the GED problem: base = 6 cm (labeled along the bottom). The small square at the foot of the dashed line confirms where height meets base.
In the GED problem: height = h (unknown, shown as dashed line). Height goes straight up from the base to the top vertex, forming a right angle.
The slanted sides of a triangle are NOT the height. The height is the perpendicular dashed line drawn inside the triangle. Always look for the right-angle square symbol (□)!
24 = ½ × 6 × h
24 = 3 × h
h = 24 ÷ 3 = 8
| Choice | How You'd Get It | Correct? |
|---|---|---|
| 8 | 24 = ½ × 6 × h → 24 = 3h → h = 8 ✅ | ✅ CORRECT |
| 9 | 24 − 6 − 9? No clear logic ❌ | ❌ Wrong |
| 4 | 24 ÷ 6 = 4 ❌ (forgot to multiply by ½ first) | ❌ Trap! |
| 2 | 24 ÷ (6 × 2) = 2 ❌ (divided by 2 instead of multiplying) | ❌ Wrong |
Many students just divide 24 ÷ 6 = 4 and stop. But the formula requires ½ × base first: ½ × 6 = 3, THEN divide area by 3 → h = 8. The ½ makes all the difference!
Starting from A = ½ × b × h, we can solve for any missing value:
Find height: h = (2 × A) ÷ b
Find base: b = (2 × A) ÷ h
A = ½ × b × h
Replace A, b, or h with the given numbers. Leave the unknown as a variable.
Multiply ½ by the known dimension first. This gives you a simple one-step equation.
A ÷ (½ × b) = h OR A ÷ (½ × h) = b
To find the missing dimension: multiply area by 2, then divide by the known side.
Missing side = (2 × Area) ÷ known side
This works for both height and base!
Select "Find Height", enter Area = 24 and Base = 6 → should get h = 8 ✅