Question

how can we calculate the area of the striped region? choose 1 answer: a $\frac{7}{5} \times \frac{1}{2}$ b $\frac{6}{12} \times \frac{2}{10}$ c $\frac{7}{5} \times \frac{2}{10}$

Explanation:

Step1: Count total parts

There are 2 large rectangles, each divided into 5 equal - sized vertical parts. So in total, there are 10 vertical parts. The striped region covers 7 of these vertical parts. The height of the striped region is half of the total height of the rectangles.

Step2: Calculate the fraction

The fraction of the horizontal part covered by the stripes is $\frac{7}{10}$, and the fraction of the vertical part covered (height - wise) is $\frac{1}{2}$. The area of the striped region is found by multiplying these two fractions. But we can also note that if we consider the first rectangle as a whole unit divided horizontally into 5 parts and vertically into 2 parts (upper and lower halves), and count the striped parts. The total number of small rectangles formed by the horizontal and vertical divisions is $5\times2 = 10$. The number of striped small rectangles is 7. The area of the striped region is the fraction of the total area it occupies. If we consider the horizontal division of the combined rectangles into 10 parts and vertical division into 2 parts (upper and lower halves), the area of the striped region is the product of the fraction of horizontal parts covered and the fraction of vertical parts covered.
The fraction of the horizontal part covered by the stripes out of all the parts of the combined rectangles is $\frac{7}{10}$ and the vertical fraction is $\frac{1}{2}$. So the area of the striped region is $\frac{7}{10}\times\frac{1}{2}=\frac{7}{5}\times\frac{1}{2}$ (since $\frac{7}{10}=\frac{7\div2}{10\div2}=\frac{7}{5}\times\frac{1}{2}$).

Answer:

A. $\frac{7}{5}\times\frac{1}{2}$