Question

The figure above is composed of $25$ small triangles that are congruent and equilateral. If the area of $△DFH$ is $10$, what is the area of $△AFK$?

• A. $40$
• B. $42.5$
• C. $50$
• D. $52.5$
• E. $62.5$

Answer 1

The correct option is E $62.5$

Given

$△$$AFK$ is composed of $25$ small congruent and equilateral triangles.

Area of $△$$DFH$ $=$ $10$

To find area of $△$$AFK$,

Let ${}^{\prime }{x}^{\prime }$ be the area of the $△$$EFG$.

$△$$DFH$ is composed of $4$ congruent and equilateral triangles which means each of those $4$ triangles have the same area as the $△$$EFG$ which is ${}^{\prime }{x}^{\prime }$.

Now, we know

$4$ $\times$ $x$ $=$ $10$

$x$ $=$ $2.5$

As $△$$AFK$ is composed of $25$ congruent and equilateral triangles each of which have area equal to that of $△$$EFG$.

Therefore, Area of $△$$AFK$ $=$ $25$ $\times$ $x$

$=$ $25$ $\times$ $2.5$

$=$ $62.5$

Therefore, Area of $△$$AFK$ is ${}^{\prime }{62.5}^{\prime }$.