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MATH / Side CD of rectangle ABCD measures 12 meters, as shown. Each of the three triangles with a side along segment CD is an equilateral triangle. What is the total area of the shaded re…

Problem

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

problem

Side CDCD of rectangle ABCDABCD measures 12 meters, as shown. Each of the three triangles with a side along segment CDCD is an equilateral triangle. What is the total area of the shaded regions? Express your answer in simplest radical form. [asy] import olympiad; size(150); defaultpen(linewidth(0.8)); fill((2,2*sqrt(3))--(4,0)--(6,2*sqrt(3))--cycle^^(6,2*sqrt(3))--(8,0)--(10,2*sqrt(3))--cycle,gray(0.7)); draw((0,0)--(12,0)--(12,2*sqrt(3))--(0,2*sqrt(3))--cycle); draw((0,0)--(2,2*sqrt(3))--(4,0)--(6,2*sqrt(3))--(8,0)--(10,2*sqrt(3))--(12,0)); label("AA",(0,2*sqrt(3)),NW); label("BB",(12,2*sqrt(3)),NE); label("CC",(12,0),SE); label("DD",(0,0),SW); draw("12 meters", (0,2*sqrt(3) + 1)--(12,2*sqrt(3) + 1),N); [/asy]
Plain-text mathematical notation (without MathML)
Side CD of rectangle ABCD measures 12 meters, as shown. Each of the three triangles with a side along segment CD is an equilateral triangle. What is the total area of the shaded regions? Express your answer in simplest radical form. [asy]
import olympiad; size(150); defaultpen(linewidth(0.8));
fill((2,2*sqrt(3))--(4,0)--(6,2*sqrt(3))--cycle^^(6,2*sqrt(3))--(8,0)--(10,2*sqrt(3))--cycle,gray(0.7));
draw((0,0)--(12,0)--(12,2*sqrt(3))--(0,2*sqrt(3))--cycle);
draw((0,0)--(2,2*sqrt(3))--(4,0)--(6,2*sqrt(3))--(8,0)--(10,2*sqrt(3))--(12,0));
label("A",(0,2*sqrt(3)),NW); label("B",(12,2*sqrt(3)),NE); label("C",(12,0),SE); label("D",(0,0),SW);
draw("12 meters", (0,2*sqrt(3) + 1)--(12,2*sqrt(3) + 1),N);
[/asy]
Original LaTeX notation
Side $CD$ of rectangle $ABCD$ measures 12 meters, as shown. Each of the three triangles with a side along segment $CD$ is an equilateral triangle. What is the total area of the shaded regions? Express your answer in simplest radical form. [asy]
import olympiad; size(150); defaultpen(linewidth(0.8));
fill((2,2*sqrt(3))--(4,0)--(6,2*sqrt(3))--cycle^^(6,2*sqrt(3))--(8,0)--(10,2*sqrt(3))--cycle,gray(0.7));
draw((0,0)--(12,0)--(12,2*sqrt(3))--(0,2*sqrt(3))--cycle);
draw((0,0)--(2,2*sqrt(3))--(4,0)--(6,2*sqrt(3))--(8,0)--(10,2*sqrt(3))--(12,0));
label("$A$",(0,2*sqrt(3)),NW); label("$B$",(12,2*sqrt(3)),NE); label("$C$",(12,0),SE); label("$D$",(0,0),SW);
draw("12 meters", (0,2*sqrt(3) + 1)--(12,2*sqrt(3) + 1),N);
[/asy]

level

Level 5

type

Prealgebra

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Source and history

task_id
98dde868-1fcf-575f-9ecf-396b77403436
task_key
prealgebra--test--98dde868-1fcf-575f-9ecf-396b77403436
task_revision_id
1
config / split
prealgebra / test

Official source

initial import