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2 years ago

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

Mathematics

1 answer:

scoundrel [369]2 years ago

7 0

Answer:

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

Step-by-step explanation:

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)

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)

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.

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fenix001 [56]

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2 years ago

If the area of a square is 100 cm2, what is the perimeter?<br>

Vitek1552 [10]

Answer:

Step-by-step explanation:

To find the perimeter, first we need to find the side lengths.

If 100 cm is the area then we need to find what number squared is 100

10 x 10 = 100

So 10 is the side length. P= s + s + s +s

10 + 10 + 10 +10 = 40

6 0

3 years ago

The distance from Earth to the sun is about 9.3 × 10 7th power miles.

AURORKA [14]

<u>Answer:</u>

The distance from earth to sun is 387.5 times greater than distance from earth to moon.

<u>Solution:</u>

Given, the distance from Earth to the sun is about $9.3 \times 10^{7} \mathrm{miles}$

The distance from Earth to the Moon is about $2.4 \times 10^{5} \mathrm{miles}$

We have to find how many times greater is the distance from Earth to the Sun than Earth to the Moon?

For that, we just have to divide the distance between earth and sun with distance between earth to moon.

Let the factor by which distance is greater be d.

$\text { Now, } \mathrm{d}=\frac{\text { distance between sun and earth }}{\text { distance between moon and earth }}=\frac{9.3 \times 10^{7}}{2.4 \times 10^{5}}=\frac{9.3}{2.4} \times 10^{7-5}\\\\=3.875 \times 10^{2}=387.5$

Hence, the distance from earth to sun is 387.5 times greater than distance from earth to moon.

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3 years ago

suppose you buy 158,000 home. you found out the bank offers 30 year loan at 6.5% APR. What will he your monthly payment

serg [7]

Answer: $998.67

Step-by-step explanation:

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3 years ago

What percent of 75.5 is 81.54

lutik1710 [3]

If you would like to know what percent of 75.5 is 81.54, you can calculate this using the following steps:

x% of 75.5 is 81.54
x% * 75.5 = 81.54
x/100 * 75.5 = 81.54
x = 81.54 * 100 / 75.5
x = 108%

Result: 108% of 75.5 is 81.54.

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3 years ago