Difference between revisions of "2024 AMC 10A Problems/Problem 22"
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==Problem== | ==Problem== | ||
Let <math>\mathcal K</math> be the kite formed by joining two right triangles with legs <math>1</math> and <math>\sqrt3</math> along a common hypotenuse. Eight copies of <math>\mathcal K</math> are used to form the polygon shown below. What is the area of triangle <math>\Delta ABC</math>? | Let <math>\mathcal K</math> be the kite formed by joining two right triangles with legs <math>1</math> and <math>\sqrt3</math> along a common hypotenuse. Eight copies of <math>\mathcal K</math> are used to form the polygon shown below. What is the area of triangle <math>\Delta ABC</math>? | ||
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<math>\textbf{(A) }2+3\sqrt3\qquad\textbf{(B) }\dfrac92\sqrt3\qquad\textbf{(C) }\dfrac{10+8\sqrt3}{3}\qquad\textbf{(D) }8\qquad\textbf{(E) }5\sqrt3</math> | <math>\textbf{(A) }2+3\sqrt3\qquad\textbf{(B) }\dfrac92\sqrt3\qquad\textbf{(C) }\dfrac{10+8\sqrt3}{3}\qquad\textbf{(D) }8\qquad\textbf{(E) }5\sqrt3</math> | ||
Revision as of 16:15, 8 November 2024
Problem
Let 
be the kite formed by joining two right triangles with legs 
and 
along a common hypotenuse. Eight copies of are used to form the polygon shown below. What is the area of triangle 
?
