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2 years ago

Find the total surface area of the figure.

Mathematics

1 answer:

Ratling [72]2 years ago

7 0

Answer:

8x6x4=192. So, the answer is 192.

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Helpppp pleaseeeeeeeeeeeeeee

Vesna [10]

Answer:

Find below the calculations of the two areas, each with two methods. The results are:

Upper triangle:

$Area=5000\sqrt{3}units^2$

Lower triangle:

$Area=14,530m^2$

Explanation:

A) Method 1

When you are not given the height, but you are given two sides and the included angle between the two sides, you can use this formula:

$Area=side_1\times side_2\times sin(\alpha)$

Where, $\alpha$ is the measure of the included angle.

1. Upper triangle:

$side_1=200units\\ \\ side_2=100units\\ \\ \alpha =60\º\\ \\ Area=200units\times 100units\times sin(60\º)/2\\ \\ Area=5000\sqrt{3}units^2$

2. Lower triangle:

$side_1=231m\\ \\ side_2=150m\\ \\ \alpha =123\º\\ \\ Area=231m\times 150m\times sin(123\º)/2\\ \\ Area=14,529.96m^2\approx14,530m^2$

B) Method 2

You can find the height of the triangle using trigonometric properties, and then use the very well known formula:

$Area=(1/2)\times base\times height$

Use it for both triangles.

3. Upper triangle:

The trigonometric ratio that you can use is:

$sine(\alpha)=opposite\text{ }leg/hypotenuse$

Notice the height is the opposite leg to the angle of 60º, and the side that measures 100 units is the hypotenuse of that right triangle. Then:

$sin(60\º)=height/100units\\ \\ height=sin(60\º)\times100units\\ \\ height=50\sqrt{3}units$

$Area=(1/2)\times base\times height=(1/2)\times 200units\times 50\sqrt{3}units=5,000\sqrt{3}units^2$

3. Lower triangle:

$sin(180\º-123\º)=height/231m\\ \\ height=sin(57\º)\times 231m\\ \\ height=193.7329m^2$

$Area=(1/2)\times base\times height=(1/2)\times 150m\times 193.7329m^2\\\\ Area=14,529.96m^2\approx 14,530m^2$

5 0

2 years ago

A triangle has vertices at (2, 3), (-4, 5), and (-3, 4). What are the coordinates of the vertices

elena-s [515]

$(2,3) \longrightarrow (2+1, 3-3)=\boxed{(3,0)}\\(-4,5) \longrightarrow (-4+1, 5-3)=\boxed{(-3, 2)}\\(-3,4) \longrightarrow (-3+1, 4-3)=\boxed{(-2, 1)}$

3 0

2 years ago

The distance between the two houses is 546m. I can walk 1.3 m/sec using the formula d=rt how long does it take to get to the hou

My name is Ann [436]

D=546m. r=1.3m/sec. 546m=1.3m/sec(t).
546m divided by 1.3m/sec = t = 420 sec (the meters will cancel out, leaving the answer to just seconds).
420 seconds divided by 60sec/min = 7 minutes.

6 0

3 years ago

Find the slope of the given information: (-5,3) and (9,-4) m = y, - y X, - X 1

dlinn [17]

Answer:

the formula is y coordinate by X coordinates

4 0

3 years ago

A camp leader figures that she needs one tent for every three campers, plus a tent for herself. Define a variable and write an e

Tomtit [17]

3t+1
The t stands for tent, and is being multiplied by 3 because there is always going to be 1 tent for every 3 campers. Plus one, for the camp leader.

6 0

3 years ago

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