Question

question #8
what percentage of the object is shaded?
a 5%
b 10%
c 15%
d 20%
question #9
stephanie ate 12 of the 40 chips in a bag. what percentage of the chips did stephanie eat?
a 12%
b 24%
c 30%
d 33%

Explanation:

Question #8

Step1: Analyze the figure

The square is divided into 5 equal - width vertical strips. Each shaded triangle: the area of a triangle is $\frac{1}{2}\times base\times height$. For the shaded triangles, if we consider the base of each triangle as the width of one strip and the height as the height of the square. The two shaded triangles can be combined (since they are in adjacent strips) to form a rectangle - like area. The total number of equal - area parts: if we think of the square's area, each of the 5 strips can be thought of as having an area that can be divided into 2 triangle - like areas (but in terms of total area, the two shaded triangles make up 1 out of 5 equal - area parts? Wait, actually, let's count the number of "triangle - units". The square has 5 vertical columns (strips). Each column can be split into 2 triangles (but the shaded ones: the first two columns have shaded triangles. The area of a triangle is $\frac{1}{2}bh$, and for the two shaded triangles, if we take the base of each as the width of one column ($w$) and height as the height of the square ($h$), then the area of one shaded triangle is $\frac{1}{2}wh$, and two of them is $wh$. The total area of the square is $5w\times h = 5wh$. So the ratio of shaded area to total area is $\frac{wh}{5wh}=\frac{1}{5}$.

Step2: Convert to percentage

To convert the fraction $\frac{1}{5}$ to a percentage, we use the formula: percentage $=\frac{1}{5}\times100\% = 20\%$? Wait, no, wait. Wait, maybe I made a mistake. Wait, let's re - examine. The square is divided into 5 equal parts (strips). Each strip can be considered as having an area. The two shaded triangles: each triangle has an area of $\frac{1}{2}$ of a strip (since area of triangle is $\frac{1}{2}\times$ base $\times$ height, and base is the width of the strip, height is the height of the square). So two triangles: $2\times\frac{1}{2}$ of a strip $ = 1$ strip. So the shaded area is 1 strip out of 5 strips. So the fraction is $\frac{1}{5}$, and $\frac{1}{5}\times100\% = 20\%$? Wait, no, wait, the answer options have D as 20%? Wait, no, wait, maybe the figure is divided into 10 small triangles? Wait, no, let's look at the figure again. The square has 5 vertical lines, creating 5 columns. In each column, there are two triangles (one on the left and one on the right? No, the first two columns have shaded triangles. Wait, maybe a better way: the total number of "triangle - shaped" regions. If we consider that the square can be divided into 10 congruent triangles (5 columns, 2 triangles per column). The shaded ones are 2 triangles. Wait, no, the two shaded triangles: if we count the number of equal - area triangles, the square has 10 small triangles (5 columns, 2 triangles per column). The shaded area is 2 triangles? No, that can't be. Wait, maybe the correct way is: the square is divided into 5 equal - width rectangles. Each rectangle has an area. The two shaded triangles: the area of each triangle is $\frac{1}{2}$ of the area of a rectangle. So two triangles have an area equal to the area of one rectangle. So the shaded area is 1 rectangle out of 5 rectangles. So the fraction is $\frac{1}{5}$, and $\frac{1}{5}\times100\% = 20\%$? Wait, but the answer is D? Wait, no, wait, maybe I messed up. Wait, let's calculate the percentage. If the shaded area is $\frac{1}{5}$ of the total area, $\frac{1}{5}=0.2$, and $0.2\times100\% = 20\%$. So the answer is D.

Step1: Use the percentage formula

The formula for percentage is $\text{Percentage}=\frac{\text{Part}}{\text{Whole}}\times100\%$. Here, the part is the number of chips Stephanie ate (12), and the whole is the total number of chips (40).

Step2: Substitute the values

Substitute part = 12 and whole = 40 into the formula: $\text{Percentage}=\frac{12}{40}\times100\%$.
First, simplify $\frac{12}{40}=\frac{3}{10}=0.3$.
Then, $0.3\times100\% = 30\%$.

Answer:

D. 20%

Question #9