Math · Geometry
Composite shape area and perimeter calculator.
Pick a combined shape (L-shape, house, arched window, rectangle with a hole), enter its lengths and get area and perimeter with the working.
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Area and perimeter
Enter the lengths.
How to find the area and perimeter of a composite shape
A composite shape is built from simpler shapes. Split it into rectangles, triangles and circles, find each area, and add them (or subtract a cut-out). The perimeter is the distance around the outside edge only; edges where two parts join are inside the shape and are not counted.
L-shape. A 10 by 8 rectangle with a 4 by 3 corner removed has an area of 10 × 8 − 4 × 3 = 68. The perimeter is still 2 × (10 + 8) = 36, because a rectangular corner cut-out replaces the removed edge with edges of the same total length.
House shape. A 6 by 4 rectangle with a triangle of height 4 on top has an area of 6 × 4 + ½ × 6 × 4 = 36. Each sloping side is √(3² + 4²) = 5, so the perimeter is 6 + 2 × 4 + 2 × 5 = 24.
Semicircle on top. A 4 by 5 rectangle with a semicircle of diameter 4 has an area of 20 + ½ × π × 2² = 26.2832 and a perimeter of 4 + 2 × 5 + π × 2 = 20.2832. Rectangle with a hole. A 10 by 6 rectangle with a hole of radius 1 has an area of 60 − π = 56.8584; the outer perimeter is 32 and the hole adds an edge of 6.2832.
The formulas used: rectangle area = width × height, triangle area = ½ × base × height, circle area = πr², rectangle perimeter = 2 × (a + b), circumference = 2πr.
Frequently asked questions
How do you find the area of a composite shape?
Split it into simple shapes such as rectangles, triangles and circles, find each area, then add the parts together or subtract any cut-out.
How do you find the perimeter of a composite shape?
Add up the lengths of the outside edges only. Edges where two parts meet are inside the shape and are left out.
Why is the perimeter of an L-shape the same as the full rectangle?
Cutting a rectangular corner out moves two sides inward but removes the same total length, so the 10 by 8 L-shape still has a perimeter of 36.
What is the area of a rectangle with a semicircle on top?
Add the rectangle area to half of a circle with the same diameter as the rectangle width. For a 4 by 5 rectangle that is 20 + 6.2832 = 26.2832.
Does the result use exact pi?
It uses the full-precision value of pi in your browser, then rounds the display to four decimal places.
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For learning
Triangles are assumed isosceles (roof peak centered). Area units are squared; perimeter units are not. Results are rounded for display. Check with your teacher's required method when you hand in homework.