Please help! This is for Algebra 1
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Answer:
Formula of Trapezoid:
A = (a + b) × h / 2
The formula can be derived in different ways. for now, we have discussed two ways:
1. By using the formula of a triangle
2. By dividing into different sections
Step-by-step explanation:
1. By using the formula of a triangle
One of the ways to explain a formula for an area of a trapezoid using a formula for a triangle can be as follows.
Assume a trapezoid PQRS with lower base SR and upper base PQ (they are parallel) and sides PS and QR.
The image is attached below.
Connect vertices P and R with a diagonal.
Consider triangle ΔPQR as having a base PQ and an altitude from vertex R down to point M on base PQ (RM⊥PQ).
Its area is
S1=
Consider triangle ΔPRS as having a base SR and an altitude from vertex P up to point N on-base SR (PN⊥SR).
Its area is
S2=
Altitudes RM and PN are equal and constitute the distance between two parallel bases PQ and SR.
They both are equal to the altitude of the trapezoid h.
Therefore, we can represent areas of our two triangles as
S1=
S2=
Adding them together, we get the area of the whole trapezoid:
S=S1+S2=
which is usually represented in words as "half-sum of the bases times the altitude".
2. By dividing into different sections
Trapezoid PQRS is shown below, with PQ parallel to RS.
Figure 1 - Trapezoid PQRS with PQ parallel to RS(image is attached below.)
We are going to derive the area of a trapezoid by dividing it into different sections.
If we drop another line from Q, then we will have two altitudes namely PT and QU.
Figure 2 - Trapezoid PQRS divided into two triangles and a rectangle. (image is attached below.)
From Figure 2, it is clear that Area of PQRS = Area of PST + Area of PQUT + Area of QRU. We have learned that the area of a triangle is the product of its base and altitude divided by 2, and the area of a rectangle is the product of its length and width. Hence, we can easily compute the area of PQRS. It is clear that
=>
Simplifying, we have
=>
Factoring we have,
=>
But, is equal to
, the longer base of our trapezoid.
Hence,
We have discussed two ways by which we can derive area of a trapezoid.
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Answer:
The number of visit so that both plan cost same is 10 .
Both the plan has equivalent choice of benefit
Step-by-step explanation:
Given as :
A gym has two membership plans.
For Gold plan
The charge per month = $50
The charge per visit = $3
For Platinum plan
The charge per month = $20
The charge per visit = $6
Let The number of visit for which each plan be same = n visits
Now, According to question
<u>∵ Each plan cost to be same</u>
So,
The charge per month for gold plan+ The charge per visit × numbers of visit = The charge per month for platinum plan+ The charge per visit × numbers of visit
I.e $50 + $3 × n = $20 + $6 × n
Or, $50 - $20 = $6 × n - $3 × n
Or, $30 = ($6 - $3) × n
Or, $30 = $3 × n
∴ n =
I.e n = 10
So, The number of visits = n = 10
Now, For Gold plan
The charge per month = $50
The charge per visit = $3 × 10 = $30
So, Total charge for gold plan = $50 + $30 = $80
Similarly For Platinum plan
The charge per month = $20
The charge per visit = $6×10 = $60
So, For Platinum plan ,total charge = $20 + $60 = $80
Hence, The number of visit so that both plan cost same is 10
and both the plan has equivalent benefit. Answer