Area of Composite Figures Quiz
Questions: 16 · 10 minutes
1. A step-shaped garden is divided into two nonoverlapping rectangles measuring 6 m by 4 m and 7 m by 5 m. What is the garden's total area?
48 m²
70 m²
59 m²
83 m²
2. An L-shaped room fits inside a 14 m by 11 m rectangle. A rectangular section is missing from the upper-right corner. The remaining top edge is 8 m long, and the lower part of the right edge is 5 m high. What is the room's area?
118 m²
124 m²
82 m²
148 m²
3. Figure A is a 9 cm by 8 cm rectangle with a 3 cm by 2 cm corner removed. Figure B is an 11 cm by 6 cm rectangle. How do their areas compare?
Figure A has the greater area.
Figure B has the greater area.
The figures have equal areas.
There is not enough information to compare them.
4. A house-shaped figure has a 12 cm by 7 cm rectangular base and a triangular top with base 12 cm and perpendicular height 5 cm. What is the total area?
102 cm²
114 cm²
144 cm²
174 cm²
5. A composite banner contains a trapezoid with parallel sides of 10 cm and 6 cm and height 4 cm, joined without overlap to a 6 cm by 5 cm rectangle. What is the banner's total area?
54 cm²
94 cm²
70 cm²
62 cm²
6. A patio is the union of a 9 m by 4 m rectangle and a 5 m by 3 m rectangle. The rectangles overlap in a 2 m by 3 m region. Which calculation gives the patio's area without double-counting the overlap?
(9 × 4) + (5 × 3)
(9 × 4) + (5 × 3) − 2
(9 × 4) + (5 × 3) − (4 × 3)
(9 × 4) + (5 × 3) − (2 × 3)
7. A storage area is split into two nonoverlapping rectangles measuring 3 m by 4 m and 2 m by 5 m. What is the combined area?
22 m²
19 m²
20 m²
10 m²
8. A decorative panel consists of a square with side length 6 cm and a quarter circle of radius 6 cm attached externally without overlap. Using π = 3.14, what is the total area?
45.42 cm²
64.26 cm²
92.52 cm²
54.84 cm²
9. A sign consists of an 8 cm by 5 cm rectangle with a semicircle of diameter 8 cm attached along one 8 cm side. Using π = 3.14, what is the sign's area?
65.12 cm²
90.24 cm²
105.12 cm²
52.56 cm²
10. A composite figure contains a nonoverlapping 8 cm by 5 cm rectangle and a second rectangle measuring x cm by 3 cm. Its total area is 58 cm². What is x?
3 cm
5 cm
8 cm
6 cm
11. An L-shaped hallway is formed by the union of a 12 m by 3 m rectangle and an 8 m by 3 m rectangle. Their intersection is a 3 m by 3 m square. What is the hallway's area?
60 m²
51 m²
42 m²
54 m²
12. An L-shaped figure can be viewed as a 12 m by 9 m rectangle with a 5 m by 4 m rectangular corner removed. What is the area of the L-shape?
88 m²
68 m²
103 m²
128 m²
13. A composite figure consists of a 10 cm by 6 cm rectangle and a 4 cm by 3 cm rectangle attached along an edge without overlapping. What is its total area?
84 cm²
60 cm²
68 cm²
72 cm²
14. A 15 m by 10 m rectangular floor has a 6 m by 4 m rectangular opening that will not be tiled. How much area will be tiled?
150 m²
90 m²
126 m²
174 m²
15. A 20 m by 12 m floor contains two nonoverlapping openings measuring 4 m by 3 m and 6 m by 2 m. What usable floor area remains?
240 m²
228 m²
216 m²
264 m²
16. A student finds the area of a 10 cm by 8 cm rectangle with a 3 cm by 2 cm corner removed by calculating 80 + 6 = 86 cm². What correction is needed?
Multiply 80 by 6 instead of adding.
Subtract 6 from 80 because the corner is removed.
Divide 80 by 6 because the corner is smaller.
Subtract the corner's perimeter, 10, from 80.