Find the surface area of this prism. Round to the nearest tenth. Help, please!!!

You are building a shelf that fits in a corner. In the figure, the entire shelf is △XYZ. Each unit in the coordinate plane repre

natima [27]

Complete Question: You are building a shelf that fits in a corner in the figure the entire shelf is XYZ each unit in the coordinate plane represents one inch find the area of the shelf.

Answer:

112.5 units²

Step-by-step explanation:

Area of the shelf = ½*base*height.

The base is the distance between Z(0, 5) and Y(15, 5)

The height is the distance between X(15, 20) and Y(15, 5).

Therefore area of the shelf = ½*ZY*XY

Use the distance formula to find ZY and XY.

Distance between Z(0, 5) and Y(15, 5):

$ZY = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Let,

$Z(0, 5) = (x_1, y_1)$

$Y(15, 5) = (x_2, y_2)$

$ZY = \sqrt{(15 - 0)^2 + (5 - 5)^2}$

$AB = \sqrt{(15)^2 + (0)^2}$

$AB = \sqrt{225 + 0} = \sqrt{225}$

$AB = 15$

Distance between X(15, 20) and Y(15, 5):

$XY = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Let,

$X(15, 20) = (x_1, y_1)$

$Y(15, 5) = (x_2, y_2)$

$XY = \sqrt{(15 - 15)^2 + (5 - 20)^2}$

$XY = \sqrt{(0)^2 + (-15)^2}$

$XY = \sqrt{0 + 225} = \sqrt{225}$

$XY = 15$

Area of shelf = ½*15*15 = ½*225 = 112.5 units²

4 0

2 years ago

when camping alone , mr adam uses all of the water in 12 days, then when mrs adams and mr adams camp together they use all of th

professor190 [17]

Using the together rate, it is found that if Mrs Adams camps alone, she will use all the water in 24 hours.

<h3>What is the together rate?</h3>

The together rate is the sum of each separate rate.

In this problem, the rates are:

Together: 1/8.

Mr Adam: 1/12.

Mrs Adams: 1/x.

Hence:

$\frac{1}{12} + \frac{1}{x} = \frac{1}{8}$

$\frac{x + 12}{12x} = \frac{1}{8}$

$12x = 8x + 96$

$4x = 96$

$x = \frac{96}{4}$

$x = 24$

If Mrs Adams camps alone, she will use all the water in 24 hours.

More can be learned about the together rate at brainly.com/question/25159431

6 0

2 years ago

For any real number c, √² =<br> A. ²<br> B. cl<br> C. 1<br> D. C

aliina [53]

Answer:

answer D ( if i interpreted your question correctly )

Step-by-step explanation:

Sqrt (c^2) = √(c^2) = C

8 0

1 year ago

The perimeter of the rectangular pool is 80 feet.The length of the pool is 10 feet more than twice of the width.Find the length

AveGali [126]

Width= 10
Length= 30

Explanation: photo

7 0

2 years ago

Please help due today

sweet-ann [11.9K]

Answer:

It is a function

Step-by-step explanation:

This isn't really a step by step explanation but I'm going to explain this simply. An output can have as many inputs possible but an input can only have ONE OUTPUT(just putting emphasis on this one output, I'm not yelling). Example, the input "2" can be equal to the output of "4" depending on the equation the fuction, however, the input of "2" CAN NOT be equal to the outputs of "4" and "6" because as my Algebra teacher explained it "for every input, there is exactly one output". I hope this helps and I hope I didn't lose you in my explaination.

4 0

2 years ago