Mikä on monikulmion piiri, kun a = 4?
Understand the Problem
Kysymys kysyy monikulmion piiriä, kun a = 4. Monikulmio on kolmio, jonka sivujen pituudet ovat 2a, 5a ja 4a + 6. Piiri lasketaan laskemalla sivujen pituudet yhteen, ja lopuksi sijoittamalla a = 4.
Answer
The perimeter is $50$.
Answer for screen readers
The perimeter of the polygon is $50$.
Steps to Solve
- Determine the formula for the perimeter
The perimeter of a polygon is the sum of its side lengths. In this case, the polygon is a triangle with side lengths $2a$, $5a$, and $4a + 6$. Therefore, the perimeter $P$ is given by: $P = 2a + 5a + (4a + 6)$
- Simplify the expression for the perimeter
Combine like terms: $P = (2a + 5a + 4a) + 6$ $P = 11a + 6$
- Substitute the value of $a$ into the formula
Given that $a = 4$, substitute this value into the formula for $P$: $P = 11(4) + 6$
- Calculate the perimeter
$P = 44 + 6$ $P = 50$
The perimeter of the polygon is $50$.
More Information
The perimeter of a polygon is the total distance around its sides, and it's found by adding the lengths of all the sides together.
Tips
A common mistake is to forget to distribute when substituting the value of $a$ into the expression $4a + 6$. Also, students may make arithmetic errors when adding the terms together.
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