Can someone please help me figure out how to find the volume of this shape?

Mathematics

2 answers:

Alenkinab [10]3 years ago

8 0

in plain and short, to get the volume of a triangular prism, we simply get the area of the triangular face and multiply that by the length.

in this case hmmm let's see the triangle has sides of 12, 12 and ... well, 12 again, is an equilateral triangle, so we get that area and multiply it by 17,

$\bf \textit{area of an equilateral triangle}\\\\ A=\cfrac{s^2\sqrt{3}}{4}~~ \begin{cases} s=side's\\ \qquad length\\ \cline{1-1} s = 12 \end{cases}\implies A=\cfrac{12^2\sqrt{3}}{4}\implies A=36\sqrt{3} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \stackrel{\textit{volume of the triangular prism}}{(36\sqrt{3})(17)\approx 1060.02}~\hfill$

Phantasy [73]3 years ago

4 0

Answer:

The volume of the shape is 29376

Step-by-step explanation:

You multiply 12 x 17 and get 204 x 12 and get 2448 x 12 and get 29376.

You might be interested in

The product of (3 − 4i) and____is 25.

LiRa [457]

$(3-4i)(a+bi)=25\qquad\text{use FOIL method}\\\\(3)(a)+(3bi)+(-4i)(a)+(-4i)(bi)=25+0i\\\\3a+3bi-4ai-4bi^2=25+0i\\\\3a+3bi-4ai-4b(-1)=25+0i\\\\3a+3bi-4ai+4b=25+0i\\\\(3a+4b)+(3b-4a)i=25+0i\\.\qquad\qquad\qquad\qquad\Downarrow\\\\3a+4b=25\ and\ 3b-4a=0\\\\3b-4a=0\qquad\text{add 4a to both sides}\\\\3b=4a\qquad\text{divide both sides by 3}\\\\b=\dfrac{4}{3}a\qquad\text{substitute it to the first equation}\\\\3a+4\left(\dfrac{4}{3}a\right)=25\\\\3a+\dfrac{16}{3}a=25\qquad\text{multiply both sides by 3}$

$9a+16a=75\\\\25a=75\qquad\text{divide both sides by 25}\\\\\boxed{a=3}\qquad\text{put the value of a to}\ b=\dfrac{4}{3}a:\\\\b=\dfrac{4}{3}(3)\\\\\boxed{b=4}\\\\Answer:\ \boxed{(3-4i)\underline{(3+4i)}=25}$