Given: ABCD is a trapezoid, AB = 13,CD = 14, BC = 5, and AD = 20. Find: A of ABCD
1 answer:
Answer:
140 cm²
Step-by-step explanation:
A trapezoid consists of one rectangle and two triangles.
Now ABCD is a trapezoid. Consider two heights BE and CF.
Therefore,l BEFC will be a rectangle,
then, EF and BC would be equal and BE and CF will be equal.
EF = BC = 5 and BE = CF = y.
Considering AE as 'x', then
FD = AD - AE - EF
FD= 20 - x - 5 => 15 - x.
Below the attactment you can see, Triangles ABE and CDF are two right triangles. Applying the Pythagorean theorem,
AB² = BE² + AE² => 13² = y² +x² ---> eq(1)
CD² = CF² + DF² => 14²= (15-x)²+ y²--->eq(2)
subtract eq (1) from eq (2)
14²-13² =(15-x)²-x²----> (term y² cancelled)
196 - 169 = 225 - 30x + x²- x² ----> (term x² cancelled)
30x= 225 - 196 + 169
30x = 198
x= 198/30 => 6.6
putting the above value in eq(1)
169= 6.6² + y²
y² = 169 - 43.56
y²= 125.44 ---> taking sqare root on both sides
y= 11.2
Area of trapezoid can be determined by
A= (5+20)/2 . 11.2 = 140
Therefore Area of trapezoid is 140 cm²
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Answer:
See below
Step-by-step explanation:
Permutation is to select an object then arrange it and it cares about the orders while Combination is about only selecting an object without caring the orders.
Permutation can be expressed in math as:
where n is a number of total object and r is a number of selected object to arrange. Hence. n cannot be less than r.
Now let's see an example of permutation, suppose we have letter A, B and C. I'd like to know how many ways these words can be arranged:
Since there are 3 letters total and 3 selected letters to arrange then:
Therefore, there are 6 ways to arrange the letters - we can also demonstrate visually:
ABC - 1
ACB - 2
BAC - 3
BCA - 4
CAB - 5
CBA - 6
Notice that if you do visually, you'll get the same answer as the calculation of permutation!
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Combination can be expressed mathematically as:
The difference between permutation and combination is that you only find how many ways you can select object in combination. Therefore, no arrange and doesn't care about order, just ways to select.
Suppose we have same 3 letters: A, B and C. I want to find how many ways I can select these 3 letters:
Since there are 3 letters total and 3 selected letters:
Hence, there is only one way to select 3 letters. This makes sense because if you have 3 letters then you can only select 3 letters only one way.