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MATH / In the diagram, △ABC is right-angled at C. Also, points M, N and P are the midpoints of sides BC, AC and AB, respectively. If the area of △APN is 2 cm², then what is the area, in s…

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Answer published by the source. Consult the official source to check your work against its answer.

problem

In the diagram, △ABC\triangle ABC is right-angled at CC. Also, points MM, NN and PP are the midpoints of sides BCBC, ACAC and ABAB, respectively. If the area of △APN\triangle APN is 2 cm22\mbox{ cm}^2, then what is the area, in square centimeters, of △ABC\triangle ABC? [asy] size(6cm); import olympiad; pair c = (0, 0); pair a = (0, 4); pair n = (0, 2); pair m = (4, 0); pair b = (8, 0); pair p = n + m; draw(a--b--c--cycle); draw(n--p--m); draw(rightanglemark(a,c,b)); label("CC", c, SW); label("AA", a, N); label("NN", n, W); label("MM", m, S); label("BB", b, E); label("PP", p, NE); [/asy]
Plain-text mathematical notation (without MathML)
In the diagram, △ABC is right-angled at C. Also, points M, N and P are the midpoints of sides BC, AC and AB, respectively.  If the area of △APN is 2 cm², then what is the area, in square centimeters, of △ABC? [asy]
size(6cm);
import olympiad;
pair c = (0, 0); pair a = (0, 4); pair n = (0, 2); pair m = (4, 0); pair b = (8, 0); pair p = n + m;
draw(a--b--c--cycle); draw(n--p--m);
draw(rightanglemark(a,c,b));
label("C", c, SW); label("A", a, N); label("N", n, W); label("M", m, S); label("B", b, E); label("P", p, NE);
[/asy]
Original LaTeX notation
In the diagram, $\triangle ABC$ is right-angled at $C$. Also, points $M$, $N$ and $P$ are the midpoints of sides $BC$, $AC$ and $AB$, respectively.  If the area of $\triangle APN$ is $2\mbox{ cm}^2$, then what is the area, in square centimeters, of $\triangle ABC$? [asy]
size(6cm);
import olympiad;
pair c = (0, 0); pair a = (0, 4); pair n = (0, 2); pair m = (4, 0); pair b = (8, 0); pair p = n + m;
draw(a--b--c--cycle); draw(n--p--m);
draw(rightanglemark(a,c,b));
label("$C$", c, SW); label("$A$", a, N); label("$N$", n, W); label("$M$", m, S); label("$B$", b, E); label("$P$", p, NE);
[/asy]

level

Level 2

type

Geometry

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Source and history

task_id
fc82bcbc-4e36-5d42-936e-a7411852f1b2
task_key
geometry--test--fc82bcbc-4e36-5d42-936e-a7411852f1b2
task_revision_id
1
config / split
geometry / test

Official source

initial import