Answer:
= 20n + 12
Step-by-step explanation:
There is a common difference d between consecutive terms, that is
d = 52 - 32 = 72 - 52 = 92 - 72 = 20
This indicates the sequence is arithmetic with explicit formula
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 32 and d = 20, thus
= 32 + 20(n - 1) = 32 + 20n - 20 = 20n + 12
we know that
The area of the hexagon is equal to the sum of the areas of the six equilateral triangles
Let
x-------> area of one equilateral triangle
so
Divide by both sides
-------> area of one equilateral triangle
To find an equivalent expression for the area of the hexagon based on the area of a triangle, multiply the area of one equilateral triangle by
therefore
the answer is
The equivalent expression is equal to