Maximum Area Calculator

Enter the required values to get accurate and quick calculations !

Maximum Area Calculator

Enter any 2 values to calculate the missing variable

Total Perimeter

in ft cm m

Maximum Side Length

in ft cm m

Maximum Area

sq in sq ft sq cm sq m

Calculate Reset

The Maximum Area Calculator lets you to  find the largest area enclosed by various shapes. Whether it’s a square, rectangle, or triangle, the knowledge of how to maximize area involves applying geometry formulas and optimization methods. With right tools to calculate the maximum area of rectangles under curves or irregular land areas, this calculator provides accurate solutions for maximizing space.

Formula:

The formula is:

$$\text{MA} = \frac{(\text{P} – 2 \times \text{SL})}{2 \times \text{SL}}$$

Variable	Meaning
MA	Maximum Area (the largest possible area that can be enclosed)
P	Perimeter (the total perimeter of the area or shape)
SL	Side Length (the length of one side or segment of the shape)

How to Calculate ?

To calculate the Maximum Area (MA):

1. Subtract twice the side length (SL) from the perimeter (P).
2. Divide the result by twice the side length (SL). This formula helps determine the largest area that can be enclosed using a given perimeter.

Solved Calculations :

Example 1:

Given:

• Perimeter (P) = 100 meters
• Side Length (SL) = 20 meters

Calculation	Instructions
Step 1: MA = $\frac{(P – 2 \times SL)}{2 \times SL}$	Start with the formula.
Step 2: MA = $\frac{(100 – 2 \times 20)}{2 \times 20}$	Replace P with 100 and SL with 20.
Step 3: MA = $\frac{(100 – 40)}{40}$	Multiply 2 by the side length and subtract it from the perimeter.
Step 4: MA = $\frac{60}{40}$	Perform the subtraction.
Step 5: MA = 1.5 square meters	Divide the result by 40.

Answer:
The maximum area is 1.5 square meters.

Example 2:

Given:

• Perimeter (P) = 80 meters
• Side Length (SL) = 15 meters

Calculation	Instructions
Step 1: MA = $\frac{(P – 2 \times SL)}{2 \times SL}$	Start with the formula.
Step 2: MA = $\frac{(80 – 2 \times 15)}{2 \times 15}$	Replace P with 80 and SL with 15.
Step 3: MA = $\frac{(80 – 30)}{30}$	Multiply 2 by the side length and subtract it from the perimeter.
Step 4: MA = $\frac{50}{30}$	Perform the subtraction.
Step 5: MA = 1.67 square meters	Divide the result by 30.

Answer:
The maximum area is 1.67 square meters.

What is Maximum Area Calculator ?

A Maximum Area Calculator lets you easily figure out the largest possible area that can be enclosed within a given set of parameters, such as perimeter or shape constraints. To find the maximum area of a shape, one typically uses optimization techniques, where calculus and geometry formulas come into play.

For example, if you’re given a fixed perimeter for a rectangle, the shape with the largest area would be a square. Similarly, the maximum area for a triangle can be calculated using specific dimensions or through optimization of a given function.

The area formula differs for each shape, and finding the maximum area depends on the shape’s properties. The rectangle, triangle, and circle are common shapes where maximizing area is often sought.

You can also calculate the maximum area of a rectangle under a curve using calculus, especially in problems involving parabolas. In cases of irregular shapes, tools like irregular land area calculators help.

To solve for maximums in Excel, you can use the MAX function to find the largest value in a dataset, which helps when dealing with a range of areas or dimensions