Hint: When you scale the linear dimensions of a figure by the factor $\lambda$, the area gets scaled by the factor $\lambda^2$. To get from the big triangle to the small one, you scale linear dimensions by the factor $\lambda=\frac{2}{5}$.
Or, in a version I like much less, take a triangle with base $b$, height with respect to that base $h$. Then new base, new height are $\lambda b$, $\lambda h$. So old area is $\frac{1}{2}bh$, new area is $\frac{1}{2}(\lambda b)(\lambda h)=\lambda^2 \frac{1}{2}bh$.
Two jokes I tell my students (though I tell them better in person) when width/height confusion strikes (don't feel bad ... it happens often!):
A guy came across his buddy in the middle of a field, desperately struggling to push a collapsible tape measure to the far-out-of-reach top of a pole sticking out of the ground. The guy asks, "If it's that important, then why don't you just knock over the pole and measure it while it lies on the ground?" His buddy responded, "Because ... I want to know how tall it is, not how long it is!"
and
A pilot and co-pilot found themselves needing to make an emergency landing on an unfamiliar airstrip. "We're coming in too fast!" warned the co-pilot, "We're going to run out of runway!" The pilot adjusted the flaps and the angle of approach to reduce speed and buy some time. "Not enough!" said the co-pilot, "We're still going to run out of runway!" The pilot made more adjustments, and more again, but the co-pilot was still frantic: "We're going to run out of runway!" In a final feat of aerodynamic magic, the masterful pilot managed to get the plane's approach speed down so that the craft touched down ever-so-gently and taxied to a safe and secure stop with its nose just past the end of the runway. "Manoman," sighed the exhausted pilot. "That's the shortest runway I've ever encountered!" "Yeah," agreed the co-pilot, "... but look how wide it is!"
... and that, my friends, is why I always endeavor to phrase the formula for the area of a parallelogram as "base-times-altitude".
Importantly, in the formula "base-time-altitude", the "base" is indeed any side you choose, but "altitude" is the altitude perpendicular to the chosen base.
So, in your problem, while $8$cm is a perfectly-good base measurement, the $6$cm measurement is not perpendicular to that base, so these numbers don't fit together into the area formula. (The altitude for the $8$cm base doesn't appear in the diagram at all.) The $6$cm measure is of the altitude perpendicular to the base of length $10$cm, so that the area is $10\times 6 = 60\text{cm}^2$.
Best Answer
This has 1 point
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This has a length of 0 cm:
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This has an area of 0 cm${}^2$:
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This has $\infty$ points
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This has a length of approximately one cm:
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This has an area of zero cm${}^2$:
$$ - $$
This has $\infty$ points
$$ \blacksquare $$
This has a length of $\infty$ cm:
$$ \blacksquare $$
This has an area of approximately one cm${}^2$:
$$ \blacksquare $$