1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Alecsey [184]
2 years ago
5

How is the formula for a triangle derived from a parallelogram? Please give a good explanation.

Mathematics
1 answer:
Katen [24]2 years ago
5 0

Answer:

At first, we divide the parallelogram into two triangles by joining any two opposite vertices. These two triangles are exactly the same (congruent) and thus have equal areas. The area of the parallelogram is the summation of the individual areas of the two triangles. We drop a perpendicular from a vertex to its opposite side to get an expression for the height of the triangles. The area of the individual triangle is 12×base×height12×base×height .The area of the parallelogram being twice the area of the triangle, thus becomes after evaluation base×heightbase×height .

Complete step by step answer:

The parallelogram can be divided into two triangles by constructing a diagonal by joining any two opposite vertices.





In the above figure, ΔABDΔABD and ΔBCDΔBCDare the two such triangles. These two triangles have:

AB=CDAB=CD (as opposite sides of a parallelogram are equal)

AD=BCAD=BC (opposite sides of a parallelogram are equal)

BDBD is common

Thus, the two triangles are congruent to each other by SSS axiom of congruence. Since, the areas of two congruent triangles are equal,

⇒area(ΔABD)=area(ΔBCD)⇒area(ΔABD)=area(ΔBCD)

Now, we need to find the area of ΔABDΔABD . We draw a perpendicular from DD to the side ABAB and name it as DEDE . Thus, ΔABDΔABD is now a triangle with base ABAB and height DEDE .

Then, the area of the ΔABD

You might be interested in
A company has two large computers. The slower computer can send all the company's email in 35 minutes. The faster computer can c
Naddik [55]

The rate for the first is 1 job / 35 minutes and for the second is 1 job / 15 minutes.  So combined we get

r = 1/35 + 1/15

3×5×7r = 3 + 7 = 10

r = 10/(105) jobs per minute

We're interested in 1/r

1/r = 105/10 = 10.5 minutes per job

Answer: 10.5 minutes

4 0
2 years ago
5x-3y=-11<br> x-2y=2<br> this is for home work please help
ale4655 [162]
5x - 3y = 11 ⇒ 5x - 3y = 11  ⇒   5x - 3y = 11
  x - 2y = 2   ⇒ -5(x - 3y) = 2 ⇒ <u>-5x + 15y = 2</u>
                                                           <u>12y</u> = <u>13</u>
                                                            12     12
                                                             y = 1 1/12
                                                 5x - 3(1 1/12) = 11
                                                 5x - 3 1/4 = 11
                                                <u>      +3 1/4    +3 1/4</u>
                                                            <u> 5x</u> = <u>14 1/4</u>
                                                              5          5
                                                               x = 2 17/20
                                                 (x, y) = (2 17/20, 1 1/12)
8 0
2 years ago
What's 46.82 rounded to the nearest ten?
NeTakaya
50 is 46.82 rounded to the nearest ten
3 0
3 years ago
Help plz I have 14 extra min!
Troyanec [42]

Answer:

20 dvds

Step-by-step explanation:

find how much each block is worth

8 blocks= 32

32/8=4

each block is worth 4

how much is 5 blocks equal to?

5(4)=20

4 0
2 years ago
if Lydia buys 1/2 pound of the Breakfast Tea and 2 pounds of the Dark Roast coffee, how many 1- pound bags of Pumpkin Spice coff
const2013 [10]

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

Lydia is at a coffee shop and knows  she can spend no more than $65

before tax. She sees this price list in  the coffee shop.

Dark Roast Coffee    $7.50

Pumpkin Spice Coffee   $10.50

Breakfast Tea   $23.50

if Lydia buys 1/2 pound of the Breakfast Tea and 2 pounds of the Dark Roast coffee, how many 1- pound bags of Pumpkin Spice coffee can she buy?

Given Information:

Shopping Budge = $65

Price of   Dark Roast Coffee = $7.50

Price of Pumpkin Spice Coffee  = $10.50

Price of  Breakfast Tea  = $23.50

Amount of Breakfast Tea required = 1/2 pound

Amount of Dark Roast coffee required = 2 pounds

Required Information:

How many 1-pound  Pumpkin Spice Coffee can she buy = ?

Answer:

n = 3 bags of 1-pound Pumpkin Spice Coffee

Step-by-step explanation:

We are given that the amount of Breakfast Tea required is 1/2 pound so the cost of Breakfast Tea is

Cost of Breakfast Tea = 1/2*23.50 = $11.75

We are also given that the amount of Dark Roast coffee required is 2 pounds so the cost of Dark Roast coffee is

Cost of Dark Roast coffee = 2*7.50

Cost of Dark Roast coffee = $15

We know that total Lydia's total budget is $65

11.75 + 15 + 10.50x = 65

Where x represents the amount of Pumpkin Spice coffee required

10.50x = 65 - 11.75 - 15

10.50x = 38.75

x = 3.64 pounds

That means Lydia can buy 3.64 pounds of Pumpkin Spice coffee.

Now assuming that the Pumpkin Spice coffee is sold only in 1-pound bags then the required number of bags that Lydia can buy is

n = 3.64 pound/1-pound

n = 3.64

Since bags cannot be in fraction so

n = 3 bags

Note: we can not round off to 4 bags since that would surpass the given budged.

7 0
3 years ago
Other questions:
  • A doctor wants to know if her patients are happy with her. She decides to survey a sample of her clients. What method would be b
    10·2 answers
  • An item on sale costs 70% of the original price. If the original price was $30, what is the sale price​
    11·2 answers
  • Omg ty for the help<br><br>is this the correct way to solve for x?​
    13·1 answer
  • What is the sum of the polynomials
    7·2 answers
  • What is the quotient
    9·2 answers
  • How many solutions does the system x + y = 3 and 2x + 2y = 5 have?
    9·2 answers
  • Could someone please help me with this?
    11·2 answers
  • 3/2 + 3/2 + 3/2 = * 1/2
    6·1 answer
  • A restaurant offers three types of meats: chicken, beef,
    15·1 answer
  • If b= 62 degrees and c=24, find b.
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!