What is the perimeter of the figure?"

Mathematics

1 answer:

anyanavicka [17]3 years ago

4 0

9514 1404 393

Answer:

46 yd

Step-by-step explanation:

The sum of horizontal lengths across the top is 8+6 = 14 yd. The length across the bottom is the same, so the total of horizontal lengths is

14 yd +14 yd = 28 yd

The sum of vertical lengths at the right is the same as the sum of vertical lengths at the left, 9 yd, so the total of vertical lengths is ...

9 yd + 9 yd = 18 yd

The total of all lengths around the perimeter of the figure is ...

28 yd + 18 yd = 46 yd

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A large wooden box, as shown, has a volume of 4352 ft3. The box is a right square prism with a base with sides that each measure

notsponge [240]

<h2>Volume of a Prism</h2>

To find the volume of a prism, we can use the following formula:

$V=base\hspace{3}area*height$

Although this formula is typically used to find the volume of a prism, we can also use it to find the base area or height, as long as we re-arrange it accordingly.

For a rectangular prism, the base area is solved using the following formula:

$A=lw$ ⇒ where <em>l</em> is the length and <em>w</em> is the width

<h2>Solving the Question</h2>

We're given:

V = 4352 ft³
<em>l</em> = 16 ft
<em>w</em> = 16 ft
We need to solve for the height of the box.

First, find the base area:

$A=lw\\A=16^2\\A=256$

Therefore, the base area is equal to 256 ft².

Now, modify the volume formula to isolate the height:

$V=base\hspace{3}area*height$

⇒ Divide both sides by the base area:

$\dfrac{V}{base\hspace{3}area}=\dfrac{base\hspace{3}area*height}{base\hspace{3}area}\\\\\dfrac{V}{base\hspace{3}area}=height\\\\height=\dfrac{V}{base\hspace{3}area}$