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Masja [62]
2 years ago
13

Finding the Area of a Trapezoid in the Coordinate Plane

Mathematics
2 answers:
Oksanka [162]2 years ago
7 0

The area of the trapezoid is 118 squre units

<h3>Area of a trapezoid</h3>

The formula for calculating the area of a trapezoid is expressed as:

  • A = 0.5(a+b)h
  • a  = AD = √20
  • b = BC = √80
  • height = h = √40

Substitute into the formula

A = 0.5(√1600)*√40

A = 0.5 * 40 * √40

A = 20√40

A = 118 squre units

Hence the area of the trapezoid is 118 squre units

Larn more on area of a trapezoid here: brainly.com/question/1463152

Dmitry [639]2 years ago
7 0

Answer:

B- 42

Step-by-step explanation:

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Help me please and thank you
Fittoniya [83]

There are 650 toothpicks in a regular sized box.

That is the volume of the box = 650 toothpicks

Jumbo box is made by doubling all the dimensions.

We know volume = length * width * height = L*W*H

We double all the dimensions for Jumbo box

L becomes 2L

W become 2W

H becomes 2H

Volume of Jumbo box = 2L * 2W * 2H = 8*L*W*H

Volume of jumbo box = 8 * volume of small box

= 8 * 650= 5200

The Jumbo box holds 5200 toothpicks .

7 0
3 years ago
The sum of two numbers is 40. If the larger is divided by the smaller, the quotient is 5 and the remainder is 4. Find the number
solmaris [256]

Answer:

numbers are 33 and 7

Step-by-step explanation:

x+y=40

4y+5+y=40

5y+5=40

5y=35

y=7

x=4y+5=4(7)+5=28+5=33

6 0
3 years ago
What is the quotient of 4 divided by 9/10
kozerog [31]
The answer is 49/9 because you can first convert the fraction into a decimal and devide 4 and 0.9 and you will get 5.4 repeating and which is 49/9
3 0
3 years ago
Read 2 more answers
point b on the ground is 5 cm from point E at the entrance to Ollie's house. He is 1.8 m tall and is standing at Point D, below
enot [183]

Point B on the ground is 5 cm from point E at the entrance to Ollie's house.

Ollie is at a distance of 2.45 m from the entrance to his house when he first activates the sensor.

The complete question is as follows:

Ollie has installed security lights on the side of his house that is activated by a  sensor. The sensor is located at point C directly above point D. The area covered by the sensor is shown by the shaded region enclosed by triangle ABC. The distance from A to B is 4.5 m, and the distance from B to C is 6m. Angle ACB is 15°.

The objective of this information is:

  • To find angle CAB and;
  • Find the distance Ollie is from the entrance to his house when he first activates the sensor.

The diagrammatic representation of the information given is shown in the image attached below.

Using  cosine rule to determine angle CAB, we have:

\mathbf{\dfrac{AB}{Sin \hat {ACB}} = \dfrac{BC}{Sin \hat {CAB}}= \dfrac{CA}{Sin \hat {ABC}}}

Here:

\mathbf{\dfrac{AB}{Sin \hat {ACB}} = \dfrac{BC}{Sin \hat {CAB}}}

\mathbf{\dfrac{4.5}{Sin \hat {15^0}} = \dfrac{6}{Sin \hat {CAB}}}

\mathbf{Sin \hat {CAB} = \dfrac{Sin 15 \times 6}{4.5}}

\mathbf{Sin \hat {CAB} = \dfrac{0.2588 \times 6}{4.5}}

\mathbf{Sin \hat {CAB} = 0.3451}

∠CAB = Sin⁻¹ (0.3451)

∠CAB = 20.19⁰

From the diagram attached;

  • assuming we have an imaginary position at the base of Ollie Standing point called point F when Ollie first activates the sensor;          

Then, we can say:

∠CBD = ∠GBF

∠GBF = (CAB + ACB)      

(because the exterior angles of a Δ is the sum of the two interior angles.

∠GBF = 15° + 20.19°

∠GBF = 35.19°

Using the trigonometric function for the tangent of an angle.

\mathbf{Tan \theta = \dfrac{GF}{BF}}

\mathbf{Tan \ 35.19  = \dfrac{1.8 \ m }{BF}}

\mathbf{BF  = \dfrac{1.8 \ m }{Tan \ 35.19}}

\mathbf{BF  = \dfrac{1.8 \ m }{0.7052}}

BF = 2.55 m

Finally, the distance of Ollie║FE║ from the entrance of his bouse is:

= 5 - 2.55 m

= 2.45 m

Therefore, we can conclude that Ollie is at a distance of 2.45 m from the entrance to his house when he first activates the sensor.

Learn more about exterior angles here:

8 0
3 years ago
Find the area of the triangle. Round your answer to the nearest tenth, if necessary.
Mashcka [7]
The answer is a 80.8
4 0
3 years ago
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