Help? Find the lateral area for the prism.

Mathematics

2 answers:

Gnoma [55]3 years ago

4 0

I think the answer will be 17 square that what my friend said.

inn [45]3 years ago

4 0

The area of the two bases, the triangles: (1/2)(4)(6)(2) = 24
The rectangle that faces toward the side: (4)(8) = 32
Now we need to find the width of the rectangle facing out toward us. We can do that by using the Pythagorean Theorem: 4² + 6² = 16 + 36 = 52. The width of the rectangle is √52, so the area of the rectangle facing toward us is 8√52 = 16√13
The area of the rectangle farthest from us: (6)(8) = 48
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We now have 24 + 32 + 48 + 16√13 = 104 + 16√13 inches².
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Hope this helps!

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Find the volume of the garden shed

Leno4ka [110]

Answer:

47.3 m³

Step-by-step explanation:

The garden shed is made up of a rectangular prism and a pyramid.

<h3><u>Volume of a rectangular prism</u></h3>

$\begin{aligned}\textsf{Volume of a rectangular prism}&=\sf width \times length \times height\\&=4 \times 4 \times 2\\&=16 \times 2\\&=32\;\; \sf m^3\end{aligned}$

<h3><u>Volume of a pyramid</u></h3>

<u />

From inspection of the given diagram, the slant height of the pyramid is 3.5 m.

Calculate the perpendicular height of the pyramid using Pythagoras Theorem:

$\begin{aligned}\implies a^2+b^2&=c^2\\2^2+h^2&=3.5^2\\h^2&=8.25\\h&=\sqrt{8.25}\;\; \sf m\end{aligned}$

Therefore:

$\begin{aligned}\textsf{Volume of a pyramid}&=\dfrac{\sf length \times width \times height}{3}\\\\&=\dfrac{\sf 4 \times 4 \times \sqrt{8.25}}{3}\\\\& = 15.31883372\;\; \sf m^3\end{aligned}$

<h3><u>Volume of the garden shed</u></h3>

$\begin{aligned}\implies \textsf{Volume of shed}&=\textsf{Volume of rectangular prism}+\textsf{Volume of pyramid}\\&=32+15.31883372\\& = 47.3\;\; \sf m^3\;(nearest\;tenth)\end{aligned}$