Expressions, Equations, and Relationships>Determining the Area of Composite Figures with Multiple Shapes(TEKS.Math.7.9.C)
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Texas 7th Grade Math › Expressions, Equations, and Relationships>Determining the Area of Composite Figures with Multiple Shapes(TEKS.Math.7.9.C)
A figure consists of a rectangle (12 ft × 8 ft) with a semicircle attached to the 12 ft side. Use 3.14 for π. What is the total area of the composite figure? Round to the nearest tenth.
209.0 square feet
322.1 square feet
152.5 square feet
96.0 square feet
Explanation
Break into a rectangle and a semicircle. Rectangle: A=lw=12×8=96. Semicircle radius is r=6, so A=½πr²=½·3.14·6²=56.52. Total =96+56.52=152.52≈152.5 square feet. Distractors: adding a full circle (96+113.04), using r=12, or omitting the semicircle.
A shape is made from a square (side 10 cm) with quarter circles cut from each corner (radius 2 cm). Use 3.14 for π. What is the total area of the remaining figure? Round to the nearest hundredth.
87.44 square centimeters
93.72 square centimeters
74.88 square centimeters
100.00 square centimeters
Explanation
Square area: 10×10=100. Four quarter circles equal one full circle of radius 2, so removed area =πr²=3.14·2²=12.56. Remaining area =100-12.56=87.44 square centimeters. Distractors use half a circle, circumference instead of area, or forget to subtract.
An L-shaped figure can be formed by starting with a 15 m by 10 m rectangle and removing a smaller 5 m by 4 m rectangle from one corner. Which set of component shapes and operation correctly computes the total area?
Add the areas of a 15×10 rectangle and a 5×4 rectangle.
Subtract the area of a 5×4 rectangle from the area of a 15×10 rectangle.
Add the area of a 15×10 rectangle and a right triangle with legs 5 m and 4 m.
Subtract the area of a 5×10 rectangle from the area of a 15×10 rectangle.
Explanation
Start with the large rectangle and subtract the missing rectangle: A=15×10-5×4=150-20=130 square meters. The other choices either add instead of subtract, introduce a triangle that is not present, or subtract the wrong dimensions.
A composite figure is made by attaching a right triangle (base 4 cm, height 6 cm) to the side of a trapezoid (bases 12 cm and 6 cm, height 5 cm). The triangle and trapezoid share a side but do not overlap. What is the total area?
65 square centimeters
45 square centimeters
36 square centimeters
55 square centimeters
Explanation
Trapezoid area: A=½(b₁+b₂)h=½(12+6)·5=½·18·5=45. Triangle area: A=½bh=½·4·6=12. Total =45+12=55 square centimeters. Distractors: forgetting the triangle (45), using bh for the triangle (adds 20 to get 65), or misusing trapezoid bases.
A stadium-shaped figure consists of a rectangle (length 20 m, width 8 m) with a semicircle attached to each of the two shorter sides (diameter 8 m). Use 3.14 for π. What is the total area? Round to the nearest tenth.
210.2 square meters
185.1 square meters
361.0 square meters
109.8 square meters
Explanation
Rectangle: A=20×8=160. Two semicircles make a full circle with r=4, so circle area =πr²=3.14·4²=3.14·16=50.24. Total =160+50.24=210.24≈210.2 square meters. Distractors: using only one semicircle (adds 25.12), using r=8, or subtracting the circle.