Triangle Area Cheat Sheet
Math Reference & Study Guide
Area of a Triangle Cheat Sheet
Keep in Binder!
The Golden Formula
\( \text{Area} = \frac{1}{2} \times b \times h \)
or write it as: \( \text{Area} = \frac{b \cdot h}{2} \)
base (b) height (h)
Why the \(\frac{1}{2}\)?
Every triangle is exactly half of a rectangle with the same base and height!
Finding Base (\(b\)) & Height (\(h\)) Anywhere
Rule: \(b\) and \(h\) MUST meet at a \(90^\circ\) angle!
1. Right Triangle
base (b) height (h) slant
Easiest: The two legs forming the \(90^\circ\) corner are your base and height.
2. Acute Triangle
base (b) h
Inside: Height drops straight down from top vertex to meet the base at \(90^\circ\).
3. Obtuse Triangle
base (b) h
Outside: Follow the dotted line! Height drops vertically outside the triangle.
Danger: The Slanted Side Trap!
NEVER use slanted edges as the height. The height must always be straight perpendicular to the base line.
✗ Slanted edge ✓ Perpendicular \(h\)
Key Step: Cut It in Half!
Multiplying \(b \times h\) gives a whole rectangle. To get the triangle, always divide by 2!
\( \text{Area} = (b \times h) \div 2 \)
3-Step Attack Plan for Any Problem
1 Identify \(b\) and \(h\)
Locate the base and spot the line meeting it at a \(90^\circ\) square corner. Ignore extra slanted sides.
2 Multiply \(b \times h\)
Multiply the base by the perpendicular height.
3 Divide by 2 (\(\div 2\))
Cut the result in half to get the final area.
Mental Math Tip: If either \(b\) or \(h\) is an even number, halve it first: \( (8 \div 2) \times 7 = 4 \times 7 = 28 \)
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Independent Practice
Triangle Area Practice Challenge
Name:
Date:
Score: /12
Directions: Show your work for every problem. Write the formula and calculate the area. \(A = \frac{1}{2} b h\)
Part 1: Triangle Practice (Watch out for extra numbers!)
2 pts each
Problem 1 Right \(\triangle\)
8 cm 6 cm 10 cm
Show work:
Area =
Problem 2 Acute \(\triangle\)
14 ft 9 ft 11 ft 12 ft
Show work:
Area =
Problem 3 Obtuse \(\triangle\)
6 m 7 m 9 m
Show work:
Area =
Part 2: Quick Word Problems
2 pts each
Problem 4: Sailboat Sail
Real-World
A sail has a base of 10 ft and a height of 16 ft. Find the area of the sail.
Show work:
Area =
Problem 5: Missing Height
Solve for \(h\)
A triangle has an area of 36 and a base of 12 in. What is its height?
Show work:
Height (\(h\)) =
Part 3: Detective Mode - Spot the Mistakes!
2 pts
b = 10 cm h = 4 cm side = 5 cm
Alex wrote:
\( 10 \times 5 = 50 \)
Write Alex's 2 mistakes, then find the correct area:
1
2
Correct Area:
Self-Check: Used \(90^\circ\) height Divided by 2 Showed my steps
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