Question

The expression, involving exponents , to represent the shaded area, in square inches, diagram. Then use that expression to calculate the shaded area, in the 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))`

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)`