{"status": "success", "data": {"description_md": "Square pyramid $ABCDE$ has base $ABCD,$ which measures $3$ cm on a side, and altitude $\\overline{AE}$ perpendicular to the base$,$ which measures $6$ cm. Point $P$ lies on $\\overline{BE},$ one third of the way from $B$ to $E;$ point $Q$ lies on $\\overline{DE},$ one third of the way from $D$ to $E;$ and point $R$ lies on $\\overline{CE},$ two thirds of the way from $C$ to $E.$ What is the area, in square centimeters, of $\\triangle PQR?$\n\n$\\textbf{(A) } \\frac{3\\sqrt2}{2} \\qquad\\textbf{(B) } \\frac{3\\sqrt3}{2} \\qquad\\textbf{(C) } 2\\sqrt2 \\qquad\\textbf{(D) } 2\\sqrt3 \\qquad\\textbf{(E) } 3\\sqrt2$\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>Square pyramid  <span class=\"katex--inline\">ABCDE</span>  has base  <span class=\"katex--inline\">ABCD,</span>  which measures  <span class=\"katex--inline\">3</span>  cm on a side, and altitude  <span class=\"katex--inline\">\\overline{AE}</span>  perpendicular to the base <span class=\"katex--inline\">,</span>  which measures  <span class=\"katex--inline\">6</span>  cm. Point  <span class=\"katex--inline\">P</span>  lies on  <span class=\"katex--inline\">\\overline{BE},</span>  one third of the way from  <span class=\"katex--inline\">B</span>  to  <span class=\"katex--inline\">E;</span>  point  <span class=\"katex--inline\">Q</span>  lies on  <span class=\"katex--inline\">\\overline{DE},</span>  one third of the way from  <span class=\"katex--inline\">D</span>  to  <span class=\"katex--inline\">E;</span>  and point  <span class=\"katex--inline\">R</span>  lies on  <span class=\"katex--inline\">\\overline{CE},</span>  two thirds of the way from  <span class=\"katex--inline\">C</span>  to  <span class=\"katex--inline\">E.</span>  What is the area, in square centimeters, of  <span class=\"katex--inline\">\\triangle PQR?</span> </p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A) } \\frac{3\\sqrt2}{2} \\qquad\\textbf{(B) } \\frac{3\\sqrt3}{2} \\qquad\\textbf{(C) } 2\\sqrt2 \\qquad\\textbf{(D) } 2\\sqrt3 \\qquad\\textbf{(E) } 3\\sqrt2</span> </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": "2019 AMC 12B Problem 18", "can_next": true, "can_prev": true, "nxt": "/problem/19_amc12B_p19", "prev": "/problem/19_amc12B_p17"}}