Area of Composite Figures
Written by Adi Ackerman, Head Teacher
"Area of Composite Figures" 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: find the area of 6 composite figures by splitting them into rectangles and triangles or subtracting. 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 split a composite figure into rectangles and triangles and add their areas.
- Students will subtract a missing corner from a larger rectangle as a second strategy.
- Students will show each step in a work box and write the area in square units.
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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Find the area of 6 composite figures by splitting them into rectangles and triangles or subtracting. The directions on the page read: Find the area A of each figure and include square units. Split it into rectangles and triangles, or subtract a part. Show your work in the box. 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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