Expressions, Equations, and Relationships>Solving Problems Involving Area and Volume with Rational Dimensions(TEKS.Math.6.8.D)
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Texas 6th Grade Math › Expressions, Equations, and Relationships>Solving Problems Involving Area and Volume with Rational Dimensions(TEKS.Math.6.8.D)
A parallelogram has a base of 7.5 meters and a height of 4.2 meters. What is the area?
31.5 m^2
15.75 m^2
11.7 m^2
31.5 m^3
Explanation
Use the area formula for a parallelogram: $A = b \times h$. Substitute: $A = 7.5 \times 4.2 = 31.5$. Attach units for area: $31.5\ \text{m}^2$.
A right rectangular prism has dimensions 2½ ft by 3¾ ft by 5 ft. Calculate the volume.
93.75 ft^3
46.875 ft^3
11.25 ft^3
9.375 ft^2
Explanation
Volume of a rectangular prism: $V = \ell w h$. Convert mixed numbers: $2\tfrac{1}{2}=\tfrac{5}{2}$ and $3\tfrac{3}{4}=\tfrac{15}{4}$. Then $V=\tfrac{5}{2}\times\tfrac{15}{4}\times 5=\tfrac{375}{8}=46.875$. Units are cubic: $46.875\ \text{ft}^3$.
A trapezoid has bases 6.4 cm and 3.6 cm and a height of 4.5 cm. What is the area?
45 cm^2
32.625 cm^2
22.5 cm^2
51.84 cm^2
Explanation
Use the trapezoid area formula: $A = \tfrac{1}{2}(b_1+b_2)h$. Compute: $b_1+b_2=6.4+3.6=10$. Then $A=\tfrac{1}{2}\times 10 \times 4.5=5\times 4.5=22.5$. Label units: $22.5\ \text{cm}^2$.
A triangle has a base of 9½ inches and a height of 7¼ inches. What is the area?
68.875 in^2
8.375 in^2
34.5 in^2
34.4375 in^2
Explanation
Triangle area: $A=\tfrac{1}{2}bh$. Convert to decimals: $b=9.5$, $h=7.25$. Then $A=\tfrac{1}{2}\times 9.5\times 7.25=\tfrac{1}{2}\times 68.875=34.4375$. Units: $34.4375\ \text{in}^2$.
A rectangle measures 3.6 meters by 2.5 meters. What is the area?
4.5 m^2
9 m^2
6.1 m^2
9 m
Explanation
Rectangle area: $A=\text{length}\times\text{width}$. Compute: $A=3.6\times 2.5=9$. Attach square units: $9\ \text{m}^2$.