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Sagot :
Answer:
[tex]A_T=91in^2[/tex]Explanation: We need to find the area of the given object, and as it can be seen that it can be thought of as composed of a square and a triangle, so if we could decompose it into a square and triangle and then find the area of these two shapes individually, then the final answer would be the sum of these two individual areas:
Area of Square:
A square can be extracted out of this image and it would have the dimensions of:
[tex]\begin{gathered} h=7\text{ in} \\ w=11\text{ in } \end{gathered}[/tex]And therefore the area would be:
[tex]\begin{gathered} A_{square}=h\times w=7in\times11in=77in^2 \\ A_{square}=77in^2 \end{gathered}[/tex]Area of Triangle:
Similarly, a triangle can be extracted from the overall shape, which has the dimensions of:
[tex]\begin{gathered} h=7in \\ b=(15-11)\text{ in=4in} \end{gathered}[/tex]Similarly, the area would be:
[tex]\begin{gathered} A_{triangle}=\frac{1}{2}(h\times b)=\frac{1}{2}(7in\times4in)=\frac{28}{2}in^2=14in^2 \\ A_{triangle}=14in^2 \end{gathered}[/tex]Finally, the total area would be:
[tex]A_T=A_{triangle}+A_{square}=14in^2+77in^2=91in^2[/tex]
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