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
Tcecarenko [31]
2 years ago
5

These 3 please!!! Properties of Kites and Trapzoids exercises 1-3

Mathematics
1 answer:
scoundrel [369]2 years ago
7 0

Answer:

  1. area = 1/2(AC)(BD)
  2. yes; BE can be found using the Pythagorean theorem
  3. yes

Step-by-step explanation:

<h3>1.</h3>

Triangles ADB and CDB are congruent, so each is half the total area. The area of ADB is ...

  A = 1/2bh

  A = 1/2(DB)(1/2AC) = 1/4(DB)(AC)

The area of the kite is twice this value:

  A = 1/2(DB)(AC)

__

<h3>2.</h3>

In order to use the formula derived in part 1, we need to know the length of BE. That can be found using the Pythagorean theorem:

  BE² +AE² = AB²

We know that AE = 1/2AC, so the desired dimension is ...

  BE = √(AB² -(1/4)AC²)

Then the area of the kite is ...

  area = 1/2(DB)(AC)

  area = (1/2)(AC)(ED +√(AB² -(1/4)AC²)

__

<h3>3.</h3>

Given three sides of a triangle, the area of it can be found using Heron's formula. If you have not yet seen that in your geometry class, you can always use the Pythagorean theorem and some algebra.

As before, we need to know the lengths of the diagonals. One is given. The other can be found considering the Pythagorean relations:

  AD² = AE² +DE²

  AB² = AE² +BE²

  BE +DE = BD . . . . the sum of the horizontal diagonal lengths

Subtracting the second equation from the first gives ...

  AD² -AB² = DE² -BE²

Using the third to write an expression for DE, we get an equation for BE:

  AD² -AB² = (BD -BE)² -BE²

  AD² -AB² = BD² -2BD·BE +BE² -BE²

  (AB² +BD² -AD²)/(2BD) = BE

Substituting this into the original second equation, we can find AE, hence the area of the kite.

  AE² = AB² -((AB² +BD² -AD²)/(2BD))²

Which means the kite area is ...

  area = BD·AE = BD√(AB² -((AB² +BD² -AD²)/(2BD))²)

  area = (1/2)√(4·AB²·BD² -(AB² +BD² -AD²)²

This area formula demonstrates it is possible to find the area of the kite given the three lengths AB, BD, DA.

_____

<em>Additional comment</em>

We have no doubt that the area formula of Part 3 can be rearranged to match Heron's formula. Here, we're interested in demonstrating area can be found.

You might be interested in
Find (f/g)(x) f(x)=4x+1 g(x) =3x-4
mash [69]
Your answer is very close to being correct; however, the true answer is actually \frac{4x+1}{3x-4} without any parenthesis needed around the fraction. Notice how there is no (x) at the end.

8 0
3 years ago
HELP Will give brainliest
ad-work [718]

Answer:

i think its 18  hope it helps

Step-by-step explanation:

4 0
3 years ago
Estimate 8/9 + 4/7<br> Sum or difference
BlackZzzverrR [31]
8/9 + 4/7=1 29/63 ESTIMATE:2
8/9 - 4/7=<span>20/63 ESTIMATE:0

</span>

6 0
3 years ago
Bill wants to rent a car.Rental Company A charges $35 per day plus $0.10 per mile driven.Rental Company B charges $25 per day pl
AlexFokin [52]
The cheapest is car rental company A
6 0
3 years ago
Find each unit rate. Round to the nearest hundredth if necessary.
Vladimir79 [104]

Answer:

A. 50 B. 27.5

Step-by-step explanation:

8 0
3 years ago
Other questions:
  • Thirty percent of what number is 63.
    8·2 answers
  • John sells plain cakes for $8 and decorated cakes for $12. On a particular day, John started with a total of 100 cakes, and sold
    10·2 answers
  • Need help with #1 please it’s algebra!
    9·2 answers
  • What is (5.2 × 10^2) × (1.2 × 10^4)?    A. 6.4 × 10^8   B. 6.24 × 10^8   C. 6.4 × 10^6   D. 6.24 × 10^6
    10·2 answers
  • A certain insect can beat its wings 200 times per second. Write an equation in slope-intercept form that shows the relationship
    11·1 answer
  • Please help with test offering big points
    13·1 answer
  • What is the value of -6+-3-(-18)
    6·2 answers
  • Pls help<br> brainliest shall be given ppl
    10·1 answer
  • Which graph represents the solution to the system of inequalities?
    6·1 answer
  • For the following inequality, find a solution for the variable. Show all of your work and use complete sentences to explain the
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!