Question

this rectangle is composed of two parts, labeled 1 and 2.
5√2 in
3 in
1
3√2 in
2
what are the areas of each smaller rectangle and the large rectangle?
drag each tile to the correct location on the image. not all tiles will be used.
the area of part 1 is: square inches.
the area of part 2 is: square inches.
the area of the entire rectangle is: square inches.
30
3 + 5√2
15√2
30 + 15√2
45√2
60

Explanation:

Step1: Calculate area of part 1

The area of a rectangle is length times width. For part 1, length is \(5\sqrt{2}\) in and width is 3 in. So area \(A_1 = 3\times5\sqrt{2}\)
\(A_1 = 15\sqrt{2}\)

Step2: Calculate area of part 2

For part 2, length is \(5\sqrt{2}\) in and width is \(3\sqrt{2}\) in. Area \(A_2 = 5\sqrt{2}\times3\sqrt{2}\)
Simplify: \(5\times3\times\sqrt{2}\times\sqrt{2}= 15\times2 = 30\)

Step3: Calculate area of entire rectangle

The area of the entire rectangle is \(A_1 + A_2\). So \(A = 15\sqrt{2}+ 30=30 + 15\sqrt{2}\)

Answer:

The area of part 1 is: \(15\sqrt{2}\) square inches.
The area of part 2 is: \(30\) square inches.
The area of the entire rectangle is: \(30 + 15\sqrt{2}\) square inches.