{"status": "success", "data": {"description_md": "A pyramid has a square base $ABCD$ and vertex $E$.  The area of square $ABCD$ is $196$, and the areas of $\\triangle ABE$ and $\\triangle CDE$ are $105$ and $91$, respectively.  What is the volume of the pyramid?\n\n$\\textbf{(A)}\\ 392 \\qquad \\textbf{(B)}\\ 196\\sqrt {6} \\qquad \\textbf{(C)}\\ 392\\sqrt {2} \\qquad \\textbf{(D)}\\ 392\\sqrt {3} \\qquad \\textbf{(E)}\\ 784$<br>([[2008 AMC 12B Problems/Problem 18|Solution]])\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>A pyramid has a square base  <span class=\"katex--inline\">ABCD</span>  and vertex  <span class=\"katex--inline\">E</span> .  The area of square  <span class=\"katex--inline\">ABCD</span>  is  <span class=\"katex--inline\">196</span> , and the areas of  <span class=\"katex--inline\">\\triangle ABE</span>  and  <span class=\"katex--inline\">\\triangle CDE</span>  are  <span class=\"katex--inline\">105</span>  and  <span class=\"katex--inline\">91</span> , respectively.  What is the volume of the pyramid?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 392 \\qquad \\textbf{(B)}\\ 196\\sqrt {6} \\qquad \\textbf{(C)}\\ 392\\sqrt {2} \\qquad \\textbf{(D)}\\ 392\\sqrt {3} \\qquad \\textbf{(E)}\\ 784</span> <br/>([[2008 AMC 12B Problems/Problem 18|Solution]])</p>&#10;<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2008 AMC 12B Problem 18", "can_next": true, "can_prev": true, "nxt": "/problem/08_amc12B_p19", "prev": "/problem/08_amc12B_p17"}}