Find the area of a regular hexagon whose apothem is 1.7cm and a side length is 2cm

Mathematics

1 answer:

tia_tia [17]3 years ago

7 0

Answer: 10.2 cm^2

Step-by-step explanation:

A regular hexagon is composed of 6 regular triangles whose area is equal to half of the product of the apothem and side.

A - triangle = (1/2)(a)(s) = (1/2)(1.7 cm)(2 cm) = 1.7 cm²

Multiplying this area by 6 to get the area of the hexagon gives us the answer which is 10.2 cm².

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For this question, it is reasonable to use the foil method. In order to use FOIL we need to understand what it stands for:
F-First
O-Outside
I-Inside
L-Last
(see attachment for visual)
Let's get started.
We are given:
$(2x^2 + 3x - 6)(x - 1)$
Start by distributing the 2 first, then the 3, and then lastly the -6
(2x^2)(x)+(2x^2)(−1)+(3x)(x)+(3x)(−1)+(−6)(x)+(−6)(−1)
From here multiply the terms you have gathered from FOILING:
 $2x^3-2x^2+3x^2-3x-6x+6$

From here we combine like terms. Like terms are terms that contain the same variable and/or exponential value. For example:
3c and 4c are like terms because they have the same variables
24 and 50 are like terms because they are simply numbers without any variables.
It is best to put the like terms together in parentheses so that it is easier to combine them.
$(2x^3)+(-2x^2+3x^2)+(-3x-6x)+(6)
$
Combine:
$2x^3+x^2-9x+6
$

Final answer: $2x^3+x^2-9x+6$
If you have an further questions, please do not hesitate to comment below! Have a nice day! :)