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The angle between a diagonal and the longer base of the isosceles trapezoid MNFD is 45°. NK is an altitude to the longer base. I

Elanso [62]

Answer:

$NK \approx 7.001$ , $MK = 2$ , $MF \approx 7.001$ , $A_{AMNFD} = 49.007$

Step-by-step explanation:

According to the statement, we find the following inputs:

$\angle MDK = \angle DMF = 45^{\circ}$ (Due to the condition of isosceles trapezoid)

$MD = 9$

$NF = 5$

Given than longer base and shorter base are parallel to each other, we conclude that:

$\angle KND = 180^{\circ} -\angle NKD - \angle KDN$

$\angle KND = 180^{\circ}-90^{\circ}-45^{\circ}$

$\angle KND = 45^{\circ}$

$\angle FND = 90^{\circ}-\angle KND$

$\angle FND = 45^{\circ}$ (By definition of complementary angles)

$\angle FND = \angle NFM = 45^{\circ}$ (Due to the condition of isosceles trapezoid)

$\angle MDK = \angle DMF = \angle FND = \angle NFM = 45^{\circ}$

$\angle NOF = \angle MOD = \angle MOF = \angle FOD = 90^{\circ}$ (By definitions of complementary and vertical angles and the theorem that states that sum of internal angles within a triangle equals 180º)

$MO = DO = \frac{\sqrt{2}}{2}\cdot MD$ (By theorem for 45-45-90 Right Triangle)

$NO = OF = \frac{\sqrt{2}}{2}\cdot NF$ (By theorem for 45-45-90 Right Triangle)

If we know that $MD = 9$ and $NF = 5$ , then we find that:

$DO = MO \approx 6.364$

$NO = OF \approx 3.536$

The value of MK is obtained from the following relationship:

$MK = \frac{MD-NF}{2}$

$MK = \frac{9-5}{2}$

$MK = 2$

And the value of KD is calculated from this expression:

$KD = MD-MK$

$KD = 9-2$

$KD = 7$

Now by the Pythagorean Theorem we find that:

$NK = \sqrt{(NO+DO)^{2}-KD^{2}}$

$NK = \sqrt{9.9^{2}-7^{2}}$

$NK \approx 7.001$

And considering the symmetry characteristics of an isosceles trapezoid, we determine MF:

$MF = NO + DO \approx 7.001$

Lastly, the area of the isosceles trapezoid is determined by the following formula:

$A_{AMNFD} = NF\cdot NK + MK\cdot NK$

$A_{AMNFD} = NK\cdot (NF+MK)$

If we know that $NK \approx 7.001$ , $NF = 5$ and $MK = 2$ , then the area of the figure is:

$A_{AMNFD} = (7.001)\cdot (5+2)$

$A_{AMNFD} = 49.007$

8 0

3 years ago

What is 4 and 1/8 times 5 and 7/8

pychu [463]

Answer:

it is 5.5

Step-by-step explanation:

4+((1÷8)×5)+(7÷8)=5.5 that is how you solve it

8 0

3 years ago

Read 2 more answers

A paper company needs to ship paper to a large printing business. The paper will be

PSYCHO15rus [73]

Answer:

Step-by-step explanation:

large boxes shiped 678

small boxes shiped 563

3 0

3 years ago

If I paid $205.50 for a phone that was 70% off, then what was the original price of the phone

slega [8]

Answer:

£349.35

Step-by-step explanation:

okay so firstly add the % to 100 = 170

then do 170 divided by 100 and multiply by the total ($205.50)

this would give you $349.35 <----- this is your orignal price (before the sale 70% off)

4 0

3 years ago

Solve for 2.<br> 5x - 5<br> 1<br> r - 2<br> 3

Alborosie

Answer:

x= 13 /14

Step-by-step explanation:

Let's solve your equation step-by-step.

5x−5

x−2

=

1

3

Step 1: Cross-multiply.

5x−5

x−2

=

1

3

(5x−5)*(3)=1*(x−2)

15x−15=x−2

Step 2: Subtract x from both sides.

15x−15−x=x−2−x

14x−15=−2

Step 3: Add 15 to both sides.

14x−15+15=−2+15

14x=13

Step 4: Divide both sides by 14.

14x

14

=

13

14

x=

13

14

5 0

3 years ago