Incomplete question: Options
(a) Each triangular part and each rectangular part represents 1/2 the area of one square.
(b) Each triangular part has an area that is greater than the area of each rectangular part.
(c) Each triangular part and each rectangular part represents 1/4 the area of one square
(d) Each rectangular part has an area that is greater than the area of each triangular part.
See attachment for squares
Answer:
(a) Each triangular part and each rectangular part represents 1/2 the area of one square.
Step-by-step explanation:
Given
See attachment
Required
Which statement is true
Before the division, the area of both squares is:
[tex]Area = l * w[/tex]
After the division:
The area of the triangle is:
[tex]Area = \frac{1}{2} * base * height[/tex]
[tex]A_1 = \frac{1}{2} * l * w[/tex]
Substitute Area for l * w
[tex]A_1 = \frac{1}{2} *Area[/tex]
This equals half the area of the square
The area of the rectangle is:
[tex]Area = length * width[/tex]
The length of the rectangle is now half the length of the original square.
So, we have:
[tex]A_2 = \frac{1}{2} l * w[/tex]
Substitute Area for l * w
[tex]A_2 = \frac{1}{2} *Area[/tex]
From the values of A1 and A2, we can conclude that (a) is true
