Perimeter and Area of Polygons
Selected Reading
- Finding the perimeter or area of a rectangle in the coordinate plane
- Area of a trapezoid
- Area of a parallelogram
- Area involving rectangles and triangles
- Finding the area of a trapezoid on a grid by using triangles and rectangles
- Area of a triangle
- Finding the area of a right triangle or its corresponding rectangle
- Finding the area of a right triangle on a grid
- Area between two rectangles
- Area of a piecewise rectangular figure
- Finding the side length of a rectangle given its perimeter or area
- Word problem involving the area of a square or a rectangle
- Areas of rectangles with the same perimeter
- Distinguishing between the area and perimeter of a rectangle
- Area of a rectangle involving fractions
- Perimeter of a piecewise rectangular figure
- Finding the missing length in a figure
- Sides of polygons having the same perimeter
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- HR Interview Questions
- Effective Resume Writing
- Questions and Answers
- UPSC IAS Exams Notes
Areas of rectangles with the same perimeter
Areas of rectangles with the same perimeter
In this lesson we find areas of rectangles with same perimeters as that of given rectangles.
We are given some rectangles with certain dimensions. We find their perimeters. We are now required to find rectangles with same perimeters as those of given rectangles but with different dimensions and then find their areas also.
The rectangle below has the dimensions 9×6. Create a rectangle with the same perimeter, but a different area.
Solution
Step 1:
Perimeter of given rectangle = 2(l + w) = 2(9 + 6) = 30; Area = l × w = 9 × 6 = 54 square units
Step 2:
One possible rectangle with same perimeter has dimensions 8×7; Its perimeter = 2(7 + 8) = 30
Its area that is different = 7 × 8 = 56 square units
The rectangle below has the dimensions 8 × 4. Create a rectangle with the same perimeter, but a different area.
Solution
Step 1:
Perimeter of given rectangle = 2(l + w) = 2(8 + 4) = 24; Area = l × w = 8 × 4 = 32 square units
Step 2:
One possible rectangle with same perimeter has dimensions 7 × 5; Its perimeter = 2(7 + 5) = 24
Its area that is different = 7 × 5 = 35 square units