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Quizzes > High School Quizzes > Mathematics

Area of Composite Shapes Practice Quiz

Master composite shapes with worksheet practice problems

Difficulty: Moderate
Grade: Grade 5
Study OutcomesCheat Sheet
Paper art representing a challenging geometry quiz for high school students.

A composite figure consists of a rectangle with dimensions 5 cm by 3 cm attached to a square with side length 3 cm. What is the total area of the shape?
24 cm²
15 cm²
21 cm²
18 cm²
The area of the rectangle is 5 cm à - 3 cm = 15 cm² and the square is 3 cm à - 3 cm = 9 cm². Adding them gives a total area of 15 + 9 = 24 cm².
A composite figure consists of a rectangle (4 cm by 6 cm) with a triangle on top having a base of 4 cm and a height of 3 cm. What is the total area of the figure?
36 cm²
30 cm²
28 cm²
32 cm²
The rectangle's area is 4 cm à - 6 cm = 24 cm² and the triangle's area is ½ à - 4 cm à - 3 cm = 6 cm². Their sum equals 24 + 6 = 30 cm².
Two adjoining squares have side lengths of 4 cm and 6 cm respectively. What is the total area of this composite shape?
40 cm²
52 cm²
50 cm²
46 cm²
The smaller square has an area of 4² = 16 cm² and the larger one has an area of 6² = 36 cm². Adding these gives 16 + 36 = 52 cm².
A composite shape is made up of a rectangle with dimensions 8 cm by 5 cm and a semicircle attached to one of its sides, where the semicircle has a radius of 4 cm. What is the total area of the figure? (Use π = 3.14 and round to one decimal place)
50.1 cm²
65.1 cm²
72.1 cm²
60.1 cm²
First, compute the area of the rectangle: 8 cm à - 5 cm = 40 cm². Next, the area of the semicircle is ½ à - π à - 4² = 25.1 cm² (approximately), and together they total about 65.1 cm².
A composite shape is formed by removing a square of side 2 cm from a larger square of side 6 cm. What is the area of the remaining figure?
30 cm²
32 cm²
28 cm²
34 cm²
The larger square has an area of 6² = 36 cm² while the smaller removed square is 2² = 4 cm². Subtracting the missing part gives 36 - 4 = 32 cm².
A composite figure consists of a rectangle measuring 10 cm by 4 cm with a semicircle attached to one of its 4 cm sides. What is the total area of the figure? (Use π = 3.14 and round to one decimal)
46.3 cm²
50.3 cm²
48.3 cm²
44.3 cm²
The rectangle's area is 10 cm à - 4 cm = 40 cm². The semicircle with diameter 4 cm (radius 2 cm) has an area of ½ à - π à - 2² ≈ 6.3 cm²; their sum is approximately 46.3 cm².
A composite shape consists of a rectangle (8 cm by 5 cm) with a triangle on top that has a base of 8 cm and a height of 6 cm. What is the area of the entire shape?
60 cm²
66 cm²
62 cm²
64 cm²
The rectangle's area is 8 cm à - 5 cm = 40 cm², and the triangle's area is ½ à - 8 cm à - 6 cm = 24 cm². Therefore, the total area is 40 + 24 = 64 cm².
Calculate the area of a composite figure which is a square with a side of 10 cm from which a circular hole with radius 3 cm has been removed. (Use π = 3.14)
75.7 cm²
72.7 cm²
68.7 cm²
71.7 cm²
The square's area is 10² = 100 cm² and the circle's area is π à - 3² ≈ 28.3 cm². Subtracting the hole gives approximately 100 - 28.3 = 71.7 cm².
A composite figure is made of two overlapping rectangles each measuring 6 cm by 4 cm, which overlap over a region of 2 cm by 3 cm. What is the total area of the figure?
42 cm²
40 cm²
46 cm²
44 cm²
Each rectangle has an area of 6 à - 4 = 24 cm², so two give 48 cm². Since the overlapping area is 2 à - 3 = 6 cm² and counts twice, subtract it once to obtain 48 - 6 = 42 cm².
Find the area of a composite shape formed by a rectangle measuring 12 cm by 5 cm with a right triangle attached having legs of 5 cm and 3 cm. What is the total area?
65.5 cm²
72.5 cm²
70.5 cm²
67.5 cm²
The rectangle's area is 12 à - 5 = 60 cm² and the triangle's area is ½ à - 5 à - 3 = 7.5 cm². Adding these together gives a total area of 60 + 7.5 = 67.5 cm².
A composite figure consists of a regular hexagon with a circle inscribed in it. If the hexagon's side length is 4 cm, calculate the difference between the hexagon's area and the circle's area. (Hint: Area of regular hexagon = (3√3/2) à - side²; Circle: πr² with r = (side à - √3)/2. Use π = 3.14 and √3 ≈ 1.73)
3.9 cm²
4.9 cm²
3.1 cm²
4.1 cm²
The hexagon's area is approximately (3 à - 1.73/2) à - 16 ≈ 41.5 cm². The circle, with radius about 3.46 cm, has an area near 37.6 cm². Their difference is roughly 41.5 - 37.6 ≈ 3.9 cm².
A rectangle of length 14 cm and width 8 cm has a semicircular extension on one of its longer sides. If the semicircle's diameter equals the width of the rectangle (8 cm), what is the total area of the figure? (Use π = 3.14 and round to one decimal)
135.1 cm²
139.1 cm²
137.1 cm²
140.1 cm²
The rectangle's area is 14 à - 8 = 112 cm². The semicircle, with a radius of 4 cm, has an area of ½ à - 3.14 à - 16 ≈ 25.1 cm². Their total area is 112 + 25.1 ≈ 137.1 cm².
Determine the total area of a figure made up of a trapezoid and an attached rectangle. The trapezoid has bases of 10 cm and 6 cm and a height of 4 cm, while the rectangle measures 6 cm by 4 cm.
58 cm²
56 cm²
60 cm²
54 cm²
The trapezoid's area is ((10 + 6)/2) à - 4 = 32 cm² and the rectangle's area is 6 à - 4 = 24 cm². Adding them gives a total area of 32 + 24 = 56 cm².
A circle with a radius of 10 cm has a quarter circle removed from it. What is the area of the remaining part? (Use π = 3.14 and round to one decimal)
236.5 cm²
235.5 cm²
230.5 cm²
240.5 cm²
The entire circle's area is π à - 10² = 314 cm² and the area of the removed quarter is ¼ à - 314 = 78.5 cm². The remaining area is 314 - 78.5 = 235.5 cm².
A square with a side of 8 cm has an inscribed circle. What is the area of the region inside the square but outside the circle? (Use π = 3.14 and round to one decimal)
14.8 cm²
15.8 cm²
12.8 cm²
13.8 cm²
The square's area is 8² = 64 cm². The circle, inscribed in the square, has a diameter of 8 cm so its radius is 4 cm and an area of approximately 3.14 à - 16 = 50.2 cm². Subtracting the circle from the square gives about 64 - 50.2 = 13.8 cm².
A composite shape is made up of a rectangle measuring 20 cm by 10 cm, from which a semicircle with a diameter of 10 cm is removed from one of the shorter sides. What is the area of the remaining shape? (Use π = 3.14 and round to one decimal)
160.8 cm²
162.8 cm²
158.8 cm²
164.8 cm²
The area of the rectangle is 20 à - 10 = 200 cm². The semicircle removed has a radius of 5 cm, giving an area of ½ à - π à - 5² ≈ 39.3 cm². Subtracting the semicircle from the rectangle gives approximately 200 - 39.3 = 160.8 cm².
Find the area of a composite figure consisting of a triangle with a base of 12 cm and a height of 9 cm attached to a rectangle measuring 12 cm by 7 cm, with a circular hole of radius 3 cm removed from the overlapping region. (Use π = 3.14)
111.7 cm²
113.7 cm²
107.7 cm²
109.7 cm²
First, compute the rectangle's area (12 à - 7 = 84 cm²) and the triangle's area (½ à - 12 à - 9 = 54 cm²) for a total of 138 cm². Then, subtract the area of the circular hole, which is π à - 3² ≈ 28.3 cm², yielding 138 - 28.3 ≈ 109.7 cm².
A composite figure consists of a square with a side of 12 cm from which a quarter circle of radius 12 cm is removed from one corner. What is the area of the resulting figure? (Use π = 3.14 and round to one decimal)
35.0 cm²
33.0 cm²
31.0 cm²
29.0 cm²
The square's area is 12² = 144 cm². A quarter circle with radius 12 cm has an area of ¼ à - π à - 144 ≈ 113.0 cm². Subtracting gives 144 - 113.0 ≈ 31.0 cm².
Determine the area of a composite shape composed of a rectangle measuring 16 cm by 9 cm and an attached isosceles triangle with a base of 16 cm and height of 8 cm, from which a circular cut-out of radius 2.5 cm is removed from the triangle. (Use π = 3.14)
190.4 cm²
188.4 cm²
186.4 cm²
192.4 cm²
The rectangle's area is 16 à - 9 = 144 cm² and the triangle's area is ½ à - 16 à - 8 = 64 cm², totaling 208 cm². The circular cut-out has an area of π à - (2.5)² ≈ 19.6 cm², so the final area is 208 - 19.6 ≈ 188.4 cm².
A complex composite shape consists of three parts: a rectangle measuring 18 cm by 7 cm, a semicircle attached to the rectangle's 7 cm side, and a triangle attached to the rectangle's adjacent 18 cm side with a height of 5 cm. If none of the added shapes overlap, what is the total area of the figure? (Use π = 3.14 and round to one decimal)
192.2 cm²
190.2 cm²
188.2 cm²
194.2 cm²
The rectangle's area is 18 à - 7 = 126 cm². The semicircle, with a diameter of 7 cm (radius 3.5 cm), has an area of ½ à - π à - (3.5)² ≈ 19.2 cm², and the triangle's area is ½ à - 18 à - 5 = 45 cm². Adding these gives approximately 126 + 19.2 + 45 = 190.2 cm².
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Study Outcomes

  1. Analyze composite shapes to identify distinct geometric components.
  2. Apply area formulas to calculate the area of individual segments.
  3. Synthesize the areas of component figures to determine the total area.
  4. Evaluate problem-solving strategies to enhance accuracy in area calculations.
  5. Interpret feedback to refine approaches for future composite area challenges.

Area of Composite Shapes Worksheet Cheat Sheet

  1. Recognize Composite Shapes - Composite shapes are figures formed by combining two or more basic shapes like rectangles, triangles, or circles. Spotting these components helps you apply the right area formulas and avoid confusion in mixed figures. Learn more here
    2. splashlearn.com
  2. Decompose Into Simple Parts - When faced with a tricky figure, split it into basic shapes - rectangles, triangles, or semicircles - to tackle each area one at a time. This step-by-step breakdown turns a headache into straightforward calculations. Learn more here
    3. bbc.co.uk
  3. Master Basic Area Formulas - Know that rectangle area is length × width, triangle area is ½ × base × height, and circle area is π × radius². Having these formulas at your fingertips speeds up any composite calculation. Learn more here
    4. cuemath.com
  4. Subtract Overlaps - If shapes overlap, calculate the shared area and subtract it once to avoid double counting. This ensures your total area reflects the actual coverage. Learn more here
    5. texasgateway.org
  5. Adjust for Partial Circles - Semicircles, quarter circles, and other fractions require you to multiply πr² by the right fraction (½ for a half, ¼ for a quarter). This tweak ensures you calculate only the relevant chunk of the circle. Learn more here
    6. owlcation.com
  6. Match Your Units - Before calculating, make sure all lengths share the same unit, whether centimeters, meters, or inches. Converting early stops confusing results and keeps your arithmetic on track. Learn more here
    7. mathworksheets4kids.com
  7. Practice Different Examples - The more varied shapes you tackle, the more intuitive the process becomes. Regular practice builds your confidence to spot hidden rectangles, triangles, and circles. Learn more here
    8. geeksforgeeks.org
  8. Visualize with Grid Paper - Sketching composite shapes on graph paper helps you divide regions precisely and count squares for a quick area check. It's a handy tool for verifying your formula-based result. Learn more here
    9. mathworksheets4kids.com
  9. Double-Check Everything - Always re-run your addition and subtraction of areas to catch slip-ups. Small arithmetic errors can throw off your entire answer, so a quick review saves points. Learn more here
    10. wtmaths.com
  10. Build Intuition Through Repetition - Regularly revisiting different composite shapes embeds formulas in your mind, making responses almost automatic during tests. Before you know it, you'll breeze through any area problem. Learn more here
    11. texasgateway.org
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