Testinar Grade 7 math

Area of Composite Shapes

Students will build Grade 7 mastery of area of composite shapes using models, equations, and test-style reasoning.

CH07-04 Measurement Geometry

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Score: ____ / 8

Directions Solve each problem. Show your reasoning on the page or on separate paper. Check the answer key only after finishing.

A composite figure is made of a rectangle (\(8\) ft by \(5\) ft) with a square (\(3\) ft by \(3\) ft) attached to one side. What is the total area?
1. \(40\) ft\(^2\)
2. \(45\) ft\(^2\)
3. \(49\) ft\(^2\)
4. \(56\) ft\(^2\)
A garden is shaped like an L. It consists of a \(6\) m by \(4\) m rectangle and a \(3\) m by \(3\) m square connected at a corner. Find the total area of the garden.
1. \(12\) m\(^2\)
2. \(21\) m\(^2\)
3. \(33\) m\(^2\)
4. \(45\) m\(^2\)
A composite figure made of two rectangles stacked vertically (both \(7\) units wide and \(2\) units tall) is shown above. What is the total area?
1. \(14\) sq units
2. \(18\) sq units
3. \(24\) sq units
4. \(28\) sq units
A floor plan shows a large rectangle \((12 \text{ ft} \times 9 \text{ ft})\) with a rectangular cutout in one corner \((4 \text{ ft} \times 3 \text{ ft})\). What is the area of the remaining floor?
1. \(83\) ft\(^2\)
2. \(96\) ft\(^2\)
3. \(108\) ft\(^2\)
4. \(120\) ft\(^2\)
A trapezoid-like composite shape is formed by a \(6\) m by \(4\) m rectangle with a triangle (\(6\) m base, \(3\) m height) on top. What is the combined area?
1. \(18\) m\(^2\)
2. \(27\) m\(^2\)
3. \(30\) m\(^2\)
4. \(33\) m\(^2\)
A composite figure consists of a rectangle (\(8\) units \(\times\) \(5\) units) joined with a triangle (base \(2\) units, height \(5\) units). What is the total area?
1. \(40\) sq units
2. \(45\) sq units
3. \(50\) sq units
4. \(55\) sq units
A rectangular garden is \(10\) m wide and \(8\) m tall. A triangular section is removed from the bottom, with the triangle's base being \(10\) m and height \(2\) m. What is the remaining area?
1. \(70\) m\(^2\)
2. \(80\) m\(^2\)
3. \(90\) m\(^2\)
4. \(100\) m\(^2\)
A composite shape is formed by placing a right triangle (legs \(5\) cm and \(12\) cm) next to a \(12\) cm \(\times\) \(5\) cm rectangle. What is the total area?
1. \(30\) cm\(^2\)
2. \(60\) cm\(^2\)
3. \(90\) cm\(^2\)
4. \(150\) cm\(^2\)

Teacher and parent reference

Answer key and explanations

C. \(49\) ft\(^2\)
Decompose into two shapes: Rectangle area \(=8\times5=40\) ft\(^2\); square area \(=3\times3=9\) ft\(^2\). Add the areas: \(40+9=49\) ft\(^2\).
C. \(33\) m\(^2\)
Rectangle: \(6 \times 4 = 24\) m\(^2\); square: \(3 \times 3 = 9\) m\(^2\). Total: \(24 + 9 = 33\) m\(^2\).
D. \(28\) sq units
Decompose into two rectangles: First rectangle \(7 \times 2 = 14\) sq units. Second rectangle \(7 \times 2 = 14\) sq units. Add them: \(14 + 14 = 28\) sq units.
B. \(96\) ft\(^2\)
Start with the large rectangle: \(12 \times 9 = 108\) ft\(^2\). Subtract the cutout rectangle: \(4 \times 3 = 12\) ft\(^2\). Remaining area: \(108 - 12 = 96\) ft\(^2\).
D. \(33\) m\(^2\)
Decompose into a rectangle and a triangle. Rectangle: \(6 \times 4 = 24\) m\(^2\). Triangle: \(\frac{1}{2} \times 6 \times 3 = 9\) m\(^2\). Add: \(24 + 9 = 33\) m\(^2\).
B. \(45\) sq units
Decompose into a rectangle and a triangle. Rectangle: \(8 \times 5 = 40\) sq units. Triangle: \(\frac{1}{2} \times 2 \times 5 = 5\) sq units. Add: \(40 + 5 = 45\) sq units.
A. \(70\) m\(^2\)
Rectangle: \(10 \times 8 = 80\) m\(^2\). Triangle removed: \(\frac{1}{2} \times 10 \times 2 = 10\) m\(^2\). Remaining: \(80 - 10 = 70\) m\(^2\).
C. \(90\) cm\(^2\)
Decompose into a rectangle and a right triangle. Rectangle: \(12 \times 5 = 60\) cm\(^2\). Right triangle: \(\frac{1}{2} \times 5 \times 12 = 30\) cm\(^2\). Add: \(60 + 30 = 90\) cm\(^2\).