Question

The diagram below shows a large square with two smaller squares within it.

(Diagram)

Write an expression, involving exponents, to calculate the shaded area, in square inches, of the diagram. Then use that expression to calculate the shaded area, in square inches, of the diagram.

Answer 1

The shaded area is
`23\ in^(2)`

Explanation:

we know that

The shaded area is equal to the area of the large square minus the area of the two smaller squares

so

`A=6^(2) -(3^(2) +2^(2))\\ \\ A=(2*3)^(2) -(3^(2) +2^(2))`

`A=(2^(2))(3^(2)) -(3^(2) +2^(2))` ---> expression that represent the shaded area

Calculate the shaded area

Remember that

`3^(2)=9\\ 2^(2)=4`

substitute

`A=(4)(9) -(9 +4)\\ \\A=36-13\\ \\A=23\ in^(2)`