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MATH / In the diagram, the area of rectangle ABCD is 40. What is the area of MBCN? [asy] import olympiad; pair a = (0, 0); pair m = (4, 0); pair b = (8, 0); pair c = (8, -5); pair n = (6,…

Problem

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

problem

In the diagram, the area of rectangle ABCDABCD is 4040. What is the area of MBCNMBCN? [asy] import olympiad; pair a = (0, 0); pair m = (4, 0); pair b = (8, 0); pair c = (8, -5); pair n = (6, -5); pair d = (0, -5); draw(m--n); draw(a--b--c--d--cycle); label("AA", a, NW); label("BB", b, NE); label("CC", c, SE); label("DD", d, SW); label("MM", m, N); label("NN", n, S); label("44", midpoint(a--m), N); label("44", midpoint(m--b), N); label("22", midpoint(n--c), S); [/asy]
Plain-text mathematical notation (without MathML)
In the diagram, the area of rectangle ABCD is 40. What is the area of MBCN? [asy]
import olympiad;
pair a = (0, 0); pair m = (4, 0); pair b = (8, 0); pair c = (8, -5); pair n = (6, -5); pair d = (0, -5);
draw(m--n);
draw(a--b--c--d--cycle);
label("A", a, NW); label("B", b, NE); label("C", c, SE); label("D", d, SW);
label("M", m, N); label("N", n, S);
label("4", midpoint(a--m), N); label("4", midpoint(m--b), N);
label("2", midpoint(n--c), S);
[/asy]
Original LaTeX notation
In the diagram, the area of rectangle $ABCD$ is $40$. What is the area of $MBCN$? [asy]
import olympiad;
pair a = (0, 0); pair m = (4, 0); pair b = (8, 0); pair c = (8, -5); pair n = (6, -5); pair d = (0, -5);
draw(m--n);
draw(a--b--c--d--cycle);
label("$A$", a, NW); label("$B$", b, NE); label("$C$", c, SE); label("$D$", d, SW);
label("$M$", m, N); label("$N$", n, S);
label("$4$", midpoint(a--m), N); label("$4$", midpoint(m--b), N);
label("$2$", midpoint(n--c), S);
[/asy]

level

Level 3

type

Prealgebra

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Source and history

task_id
9bc8b1e0-1d5f-5b63-96ef-feb7670656b6
task_key
prealgebra--test--9bc8b1e0-1d5f-5b63-96ef-feb7670656b6
task_revision_id
1
config / split
prealgebra / test

Official source

initial import