Fig 1 and Fig 2 show an equilateral triangle divided into thirds and quarters respectively. They are combined in Fig 3. Calculate the fraction of Fig 3 that is shaded.

\frac{7}{12}

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\frac{5}{12}

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\frac{5}{24}

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\frac{11}{24}

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Solution

The correct option is D $\frac{5}{24}$
In fig 1, the figure is divided into three equal parts . So, the value of each part is $\frac{1}{3}$
In fig 2, the figure is divided into four equal parts. So, the value of each part is $\frac{1}{4}$
Now, in figure 3, value of shaded region is
$= \frac{1}{4} \times \frac{1}{2} + \frac{1}{3} \times \frac{1}{4} = \frac{1}{8} + \frac{1}{12} = \frac{5}{24}$
So, correct answer is option C.

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