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WINSTONCH [101]
3 years ago
9

Find the area of the regular octagon if the apothem is 4.2 and a side is 3.4 In. Round to the nearest whole number. A. 114 B. 57

C. 157 D. 94

Mathematics
2 answers:
tatuchka [14]3 years ago
7 0

Answer:

B. 57\text{ in}^2

Step-by-step explanation:

We have been that apothem of a regular octagon is 4.2 inches and length of each side is 3.4 inches. We are asked to find the area of our given octagon.

We know that area of octagon is half the product of perimeter and apothem of the octagon.

\text{Area of octagon}=\frac{1}{2}\times (a\cdot p), where,

a = Apothem of octagon,

p = perimeter of octagon.

We will find perimeter of our given octagon by multiplying length of each side by 8.

\text{Perimeter of octagon}=8\times 3.4\text{ in}

\text{Perimeter of octagon}=27.2\text{ in}

\text{Area of octagon}=\frac{1}{2}\times (4.2\text{ in}\cdot 27.2\text{ in})

\text{Area of octagon}=\frac{1}{2}\times (114.24\text{ in}^2)

\text{Area of octagon}=57.12\text{ in}^2\approx 57\text{ in}^2

Therefore, the area of our given octagon is 57 square inches and option B is the correct choice.

Elena-2011 [213]3 years ago
6 0
The area of the regular octagon is calculated as half of the product of the perimeter and the apothem (ap), using the formula of the area of the regular polygon.
 We have then:
 A = ((p) * (ap)) / 2
 Where,
 p: perimeter
 ap: apotema
 Substituting values:
 A = ((8 * 3.4) * (4.2)) / 2
 A = 57.12 in ^ 2
 Answer:
 
the area of the regular octagon is:
 
B. 57
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5 0
2 years ago
Find all real zeros of f(x) = 2x^2 +5x-18 algebraically.
den301095 [7]
2x2-5x-18=0

Two solutions were found :

x = -2
x = 9/2 = 4.500
Step by step solution :

Step 1 :

Equation at the end of step 1 :

(2x2 - 5x) - 18 = 0
Step 2 :

Trying to factor by splitting the middle term

2.1 Factoring 2x2-5x-18

The first term is, 2x2 its coefficient is 2 .
The middle term is, -5x its coefficient is -5 .
The last term, "the constant", is -18

Step-1 : Multiply the coefficient of the first term by the constant 2 • -18 = -36

Step-2 : Find two factors of -36 whose sum equals the coefficient of the middle term, which is -5 .

-36 + 1 = -35
-18 + 2 = -16
-12 + 3 = -9
-9 + 4 = -5 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -9 and 4
2x2 - 9x + 4x - 18

Step-4 : Add up the first 2 terms, pulling out like factors :
x • (2x-9)
Add up the last 2 terms, pulling out common factors :
2 • (2x-9)
Step-5 : Add up the four terms of step 4 :
(x+2) • (2x-9)
Which is the desired factorization

Equation at the end of step 2 :

(2x - 9) • (x + 2) = 0
Step 3 :

Theory - Roots of a product :

3.1 A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.
4 0
3 years ago
Read 2 more answers
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