Question

1. what do you notice and wonder about the methods used below to determine the area.
2. share with your partner how to determine the area for the following figure.

Explanation:

Step1: Recall area formula for rectangle

The area formula for a rectangle is $A = l\times w$, where $l$ is the length and $w$ is the width.

Step2: For problem 3

The length of the rectangle is $\sqrt{50}=\sqrt{25\times2} = 5\sqrt{2}$ and the width is $2\sqrt{2}$. Using the area formula $A=(5\sqrt{2})\times(2\sqrt{2})$. By the property of square - roots $\sqrt{a}\times\sqrt{a}=a$ and multiplication of real - numbers, $A = 5\times2\times\sqrt{2}\times\sqrt{2}=20$ square units. Also, when divided into smaller rectangles of area $2$ square cm each, there are 10 such rectangles, and $10\times2 = 20$ square cm.

Step3: For problem 4

The length of the rectangle is $\sqrt{243}=\sqrt{81\times3}=9\sqrt{3}$ and the width is $3\sqrt{3}$. Using the area formula $A=(9\sqrt{3})\times(3\sqrt{3})$. Since $\sqrt{3}\times\sqrt{3}=3$, then $A=9\times3\times3 = 81$ square units. Also, if we consider the small rectangles of area 3 square units each, we need to find out how many are there. The area of the large rectangle is 81 square units, and $\frac{81}{3}=27$ small rectangles of area 3 square units each would make up the large rectangle.

Answer:

For problem 3, the area is 20 square units. For problem 4, the area is 81 square units.