Same Perimeter, Different Area
Written by Adi Ackerman, Head Teacher
"Same Perimeter, Different Area" is written for 8th Grade (Ages 13-14). A 7th grader who is already steady on geometry can use it too, and an older student can use it as a short review.
8th grade math worksheet: compare rectangles with the same perimeter or the same area, such as two pens made from 50 m of fence. Answer key included. Part of our perimeter and area geometry collection.
How do I use this worksheet?
Start with Perimeter of Polygons and Area of Triangles and Quadrilaterals, then move to the coordinate and missing side sheets. Use Area and Perimeter Review or Area Riddle as a check at the end.
What students will practice
- Students will compare the areas of rectangles that share the same perimeter.
- Students will compare the perimeters of rectangles that share the same area.
- Students will complete a table to find which length and width give the most area.
Curriculum Links
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FAQ
How do I use this perimeter and area worksheet?
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Start with Perimeter of Polygons and Area of Triangles and Quadrilaterals, then move to the coordinate and missing side sheets. Use Area and Perimeter Review or Area Riddle as a check at the end.
What does this worksheet teach?
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Compare rectangles with the same perimeter or the same area, such as two pens made from 50 m of fence. The directions on the page read: Rectangles with the same perimeter can have different areas, and rectangles with the same area can have different perimeters. Solve each problem and include units. The page opens with a worked example, and an answer key is included.
Can I use this perimeter and area worksheet for homeschool or classroom?
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Yes, both. We made it for 8th grade geometry, and it works the same at home or at school. At home, a student can work through it alone and then go over it with you, which shows quickly what is solid and what needs another look. In class it works as independent practice, homework or a warm-up, and you can print one copy or a full set.
What is the difference between area and perimeter?
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Perimeter adds the lengths around a figure and is measured in units like feet. Area measures the space inside and is measured in square units like square feet. Area and Perimeter Word Problems asks students to decide which one each situation needs, such as fence around a garden or paint on a wall.
How do you find the perimeter of a figure on a coordinate plane?
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Count the length of each horizontal and vertical side from the coordinates. Use the Pythagorean theorem for slanted sides, then add all the sides. In the example on Perimeter on the Coordinate Plane, sides of 7, 2 and the square root of 53 give a perimeter of about 16.3 units.
How do you find a missing side when you know the perimeter?
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Write an equation that sets the sum of the sides equal to the perimeter, then solve it. For a rectangle 8.4 m by x m with a perimeter of 30 m, 2x + 16.8 = 30, so x = 6.6. Find a Missing Side From the Perimeter has 8 figures like this.
Can two rectangles have the same perimeter but different areas?
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Yes. With a perimeter of 34 cm, an 11 by 6 rectangle has an area of 66 cm², while an 8.5 by 8.5 square has 72.25 cm². Same Perimeter, Different Area also compares rectangles that share an area but not a perimeter.
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