Clarissa 2

Clarissa is cutting construction paper into rectangles for a project. She needs to cut one 12 inches x 15 1/3 inches rectangle. She needs to cut another rectangle 10 1/4 inches by 10 1/3 inches. How many Total square inches of construction paper does Clarissa need for her project?

Final Answer:

A =  289 ¹¹⁄₁₂ = 3479/12 in²

Step-by-step explanation:

$$\begin{gathered} a=12\text{in} \\ b=15\frac{1}{3}=15+\frac{1}{3}=\frac{15\cdot 3+1}{3}=\frac{45+1}{3}=\frac{46}{3}\doteq 15.3333\text{in} \\ x=10\frac{1}{4}=10+\frac{1}{4}=\frac{10\cdot 4+1}{4}=\frac{40+1}{4}=\frac{41}{4}=10.25\text{in} \\ y=10\frac{1}{3}=\frac{31}{3}\doteq 10.3333\text{in} \\ {A}_1=a\cdot b=12\cdot \frac{46}{3}=\frac{12\cdot 46}{3}=\frac{552}{3}=184{\text{in}}^2 \\ {A}_2=x\cdot y=\frac{41}{4}\cdot \frac{31}{3}=\frac{41\cdot 31}{4\cdot 3}=\frac{1271}{12}\doteq 105.9167{\text{in}}^2 \\ A=A_1+A_2=184+\frac{1271}{12}=\frac{184\cdot 12}{12}+\frac{1271}{12}=\frac{2208}{12}+\frac{1271}{12}=\frac{2208+1271}{12}=\frac{3479}{12}=\frac{3479}{12}{\text{in}}^2=289\frac{11}{12}{\text{in}}^2=289.9167{\text{in}}^2 \end{gathered}$$

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