Base of a Triangle Calculator
Calculate the base of a triangle using its area and height
Triangle Calculator
Area (Known)
Height (Known)
Base (Result)
Calculation Result
Triangle Summary
Step-by-Step Solution
Step 1: Use the base formula b = 2 × A / h Step 2: Substitute the known values Area (A) = 60 cm² Height (h) = 15 cm Step 3: Calculate the base b = 2 × 60 / 15 b = 120.00 / 15 b = 8.0000 cm The base of the triangle is 8.0000 cm.
Formula Used
Where b is base, A is area, and h is height
Example Calculations
Example 1: Finding the Base
Problem: A triangle has an area of 60 cm² and height of 15 cm. Find the base.
Formula: b = 2A / h
Solution: b = 2 × 60 / 15 = 120 / 15 = 8 cm
Answer: The base is 8 cm
Example 2: Finding the Area
Problem: A triangle has base 10 cm and height 6 cm. Find the area.
Formula: A = (b × h) / 2
Solution: A = (10 × 6) / 2 = 60 / 2 = 30 cm²
Answer: The area is 30 cm²
Example 3: Finding the Height
Problem: A triangle has area 24 cm² and base 8 cm. Find the height.
Formula: h = 2A / b
Solution: h = 2 × 24 / 8 = 48 / 8 = 6 cm
Answer: The height is 6 cm
Triangle Formulas
Area Formula
A = (b × h) / 2
Base Formula
b = 2A / h
Height Formula
h = 2A / b
Triangle Properties
Base
Any side perpendicular to height
Height
Perpendicular distance to base
Area
Space enclosed by triangle
Quick Tips
Any side can be chosen as the base
Height must be perpendicular to chosen base
All formulas are derived from A = bh/2
Works for all triangle types
Understanding Triangle Base Calculations
What is the Base of a Triangle?
The base of a triangle is any side that is chosen as the bottom side. The height is then measured as the perpendicular distance from the opposite vertex to this base. Any of the three sides can serve as the base, depending on the orientation and calculation needs.
Base Formula Derivation
Starting with: A = (b × h) / 2
Multiply both sides by 2: 2A = b × h
Divide both sides by h: b = 2A / h
This formula allows us to find the base when we know the area and height of the triangle.
Practical Applications
Base calculations are essential in construction, architecture, and design. For example, when designing triangular shelves, roofing elements, or structural supports, you often need to determine the base length from area and height constraints.
Key Concepts
- •The height is always perpendicular to the chosen base
- •The same triangle can have three different base-height pairs
- •All calculations yield the same area regardless of chosen base
- •Formula works for acute, right, and obtuse triangles
Real-World Examples
Construction
Determining the base width of triangular trusses when the area and height specifications are given.
Landscaping
Calculating the base length of triangular garden beds with known area and available height.
Manufacturing
Designing triangular components where area constraints and height limitations determine base dimensions.
Alternative Calculation Methods
While the area-height method is most common, triangular bases can also be calculated using:
Coordinate Geometry
Using vertex coordinates to calculate base length directly with the distance formula.
Trigonometry
Using angles and other side lengths with sine, cosine, and tangent relationships.