Question

Write an expression, involving exponents to represent the shaded area, in square inches of the diagram. ​

Answer 1

The area is 21 inches

Explanation:

3x3=9

3x2=6

9+6=15 ( inches in the white box )

6x6=36 ( area of the whole box)

36-15= 21 ( inches in the shaded area )

Answer 2

`6^(2)-(3^(2)+2^(2)) =23`

Explanation:

We have got 3 squares here. The shaded area is not clear but it is an understood fact that the question must be asking about the area in the bigger square minus the sum of smaller 2 squares.

So, the area of the bigger square is =
`6^(2)` (exponent form)

or 36 square inches

Area of smaller square with side 3 inches =
`3^(2)` (exponent form)

or 9 square inches

Area of second smaller square with side 2 inches =
`2^(2)` (exponent form) or 4 square inches.

Sum of the area of smaller squares =
`3^(2) +2^(2)` = 9+4 = 13 sq inches

And area of the shaded region will be = 36-13 = 23 square inches.

In exponent form it can be written as :
`6^(2)-(3^(2)+2^(2)) =23`