We want to find the perimeter and area of the top of the child's desk. We will start by finding the perimeter and area of the top of the full-size desk. To do so, let's recall the formulas for the perimeter and area of a rectangle with length l and width w.
Perimeter of a Rectangle
2 l + 2 w
Area of a Rectangle
l w
In the case of the top of the full-size desk, l= 54 and w= 36. We can substitute these values into each formula to calculate the perimeter and area of the top of the full-size desk. Let's do it!
Perimeter, in.
2( 54) + 2( 36) = 108+72=180
Area, in^2
54 ( 36) = 1944
We got that the perimeter of the top of the full-size desk is 180 inches and the area is 1944 square inches. Next, we will recall the relationships between perimeters and areas of similar figures.
Perimeter of Similar Figures
If figure B is similar to figure A by a scale factor, then the perimeter of B is equal to the perimeter of A times the scale factor.
Area of Similar Figures
If figure B is similar to figure A by a scale factor, then the area of B is equal to the area of A times the square of the scale factor.
We know that the child's desk is made so that the dimensions are two-thirds the dimensions of the full-size desk. This means these desks are similar and the scale factor is 23. Since we know the perimeter and area of the top of the full-size desk, we can now calculate the perimeter and area of the top of the child's desk.
Perimeter, in.
180( 2/3) =120
Area, in^2
1944( 2/3)^2 =1944 (4/9)= 864
Therefore, the perimeter of the top of the child's desk is 120 inches and the area is 864 square inches.
