Find the area of the L-shaped figure. Its outer rectangle is 9 cm by 10 cm, with a 5 cm by 3 cm corner removed.
Show reasoning / computation: __________________________________________
CCSS 7.G.B.6 · area of figures built from polygons
Composite Area Worksheet Generator
Decompose or subtract familiar shapes instead of memorizing a new formula for every outline. Diagrams are dimension-driven so every labeled length matches the generated calculation.
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Composite Area
Diagrams are part of the problem data, not decorative assets. Student pages keep solution-specific marks hidden; reveal answers or use the separate PDF key to check work.
Problem 1
Problem 2
A rectangle 5 cm by 5 cm has a triangle attached along its 5-cm side. The triangle height is 5 cm. Find the total area.
Show reasoning / computation: __________________________________________
Problem 3
Find the area of the L-shaped figure. Its outer rectangle is 9 cm by 6 cm, with a 4 cm by 3 cm corner removed.
Show reasoning / computation: __________________________________________
Problem 4
Find the area of the L-shaped figure. Its outer rectangle is 10 m by 9 m, with a 6 m by 5 m corner removed.
Show reasoning / computation: __________________________________________
Problem 5
A rectangle 7 cm by 7 cm has a triangle attached along its 7-cm side. The triangle height is 5 cm. Find the total area.
Show reasoning / computation: __________________________________________
Problem 6
A rectangle 5 cm by 5 cm has a triangle attached along its 5-cm side. The triangle height is 4 cm. Find the total area.
Show reasoning / computation: __________________________________________
Problem 7
Find the area of the L-shaped figure. Its outer rectangle is 10 ft by 8 ft, with a 3 ft by 4 ft corner removed.
Show reasoning / computation: __________________________________________
Problem 8
Find the area of the L-shaped figure. Its outer rectangle is 11 ft by 10 ft, with a 6 ft by 3 ft corner removed.
Show reasoning / computation: __________________________________________
Splitting or subtracting to find area
Composite figures never need a new formula. Each one can be cut into rectangles and triangles whose areas are added, or treated as a larger rectangle with a piece removed. The diagrams here are built from their dimensions, so every labeled length agrees with the generated calculation.
Encouraging more than one method
Try solving one figure twice: once by adding parts, once by subtracting from an enclosing rectangle. Two methods that give the same area are a strong self-check, and the answer key shows both the sum and the difference form for the same figure.
Two ways to read the same figure
- A 10 by 7 rectangle with a 4 by 3 corner cut out has area 70 − 12 = 58 square units.
- An L-shape inside a 9 by 6 rectangle with a 4 by 2 corner missing has area 54 − 8 = 46 square units.
- A rectangle 8 units wide and 5 tall with a triangle on top of base 8 and height 3 has area 40 + 12 = 52 square units.
Frequent slips with composite figures
- Using the slanted side of a triangle as its height instead of the perpendicular height.
- Forgetting the one-half when finding the area of a triangle.
- Counting an overlapping region twice when decomposing a figure.
Classroom note 1
L-shaped area can be found by subtracting a missing rectangle from an outer rectangle.
Classroom note 2
A rectangle-plus-triangle figure can be decomposed and the two areas added.
Classroom note 3
Example: an 8 by 6 rectangle with a 3 by 2 corner removed has area 48 minus 6, or 42 square units.
Classroom note 4
Area answers require square units.
Continue the 7.G progression
Move to another Grade 7 geometry skill
Questions people ask
Do the diagrams match the numbers?
Yes. The SVG/PDF outline is generated from the same dimensions used in the answer.
Are these only L-shapes?
No. Seeds rotate between subtraction-style L-shapes and additive rectangle-plus-triangle figures.
Which standard does this practice?
CCSS 7.G.B.6: solve real-world and mathematical problems involving area of two-dimensional objects composed of triangles and quadrilaterals.