Grades 7-8 Video Solutions 2021-video 2021 7-8/13

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Question 13. The area of the large square is 16 centimeters squared. The area of each small square is 1 centimeter squared. What is the total area of the  black flower? Let's take a closer look at the large square, which has an area of 16 centimeters squared. This means that each side of this square has a length of 4  centimeters. Now, if we look at just one quadrant of this large square, we can break it off like this. We know that the small square has side of 1 centimeter.  Now, we know that this is a length half equal to the large square, so the square we just drew has a length of 2 centimeters on each side. This means that  2 by 2 is equal to 4 centimeters. That is the area of the square we just drew out. Now, we also know that there are some white triangles inside of the smaller  square, which have a base of 1 centimeter and a height of 2 centimeters. So the area of the white triangle will be 1 centimeter times 2 centimeters divided by  2, but we would multiply this by 2 since there are two white triangles inside of the square, giving us 2 centimeters. Next, we take a look at the area of the yellow  square, which is 1 centimeter by 1 centimeter. So the area is 1 centimeter. To get the area of the black portion inside of this square, we just have to do  the total area, 4 centimeters, minus the area of the white triangles, 2 centimeters, minus the area of the yellow square, 1 centimeter. With this, we get 1 centimeter.  Now, since we know that there are four black sections like this, we just multiply this number by 4. When we do 1 times 4, we get our answer, C, 4 centimeters squared.

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