## Which triangle has the maximum area for a given perimeter?

So the triangle that gives the maximum area for a given perimeter is an equilateral triangle. The quadrilateral that gives the maximum area for a given perimeter is a square.

## How do you find the minimum and maximum area?

To find the maximum possible area, add the greatest possible error to each measurement, then multiply. To find the minimum possible area, subtract the greatest possible error from each measurement, then multiply.

How do you find the maximum area of a shape?

A rectangle will have the maximum possible area for a given perimeter when all the sides are the same length. Since every rectangle has four sides, if you know the perimeter, divide it by four to find the length of each side. Then find the area by multiplying the length times the width.

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Which triangle has minimum area?

I think, the isosceles triangle will have minimum area. Let, the each side of the equilateral triangle be 2a. So, the perimeter of the triangle is 6a. Therefore, area of the equilateral triangle is {(√3)*(a^2)}.

### How do you find maximum and minimum values in geometry?

To find the maximum possible volume, add the greatest possible error to each measurement, then multiply. To find the minimum possible volume, subtract the greatest possible error from each measurement, then multiply.

How do you find the area of a 45 degree triangle?

When t = 45 degrees, the area of the inscribed right triangle is maximum. The length of sides AB and CB are given by AB = AC * cos (45 degrees) = 2 r sqrt (2) and CB = AC * sin (45 degrees) = 2 r sqrt (2)

When is the area of a triangle maximum for a perimeter?

Area of a triangle is maximum for a given perimeter when it is a equilateral (nature loves symmetry). This can be proved by concept of maxima! The area of a triangle = 0.5 *base* height.