2019 AMC 8 Problems/Problem 21

Problem 21

What is the area of the triangle formed by the lines $y=5$ , $y=1+x$ , and $y=1-x$ ?

$\textbf{(A) }4\qquad\textbf{(B) }8\qquad\textbf{(C) }10\qquad\textbf{(D) }12\qquad\textbf{(E) }16$

Solution 1

You need to first find the coordinates where the graphs intersect. y=5, and y=x+1 intersect at (4,5). y=5, and y=1-x intersect at (-4,5). y=1-x and y=1+x intersect at (1,0). Using the Shoelace Theorem you get $\left(\frac{(20-4)-(-20+4)}{2}\right)$ = $\frac{32}{2}=$ \boxed{\textbf{(E)}\ 16}$.

2019 AMC 8 (Problems • Answer Key • Resources)
Preceded by Problem 20	Followed by Problem 22
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2019 AMC 8 Problems/Problem 21

Problem 21

Solution 1

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