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MATH / By joining alternate vertices of a regular hexagon with edges 4 inches long, two equilateral triangles are formed, as shown. What is the area, in square inches, of the region that …

Problem

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

problem

By joining alternate vertices of a regular hexagon with edges 44 inches long, two equilateral triangles are formed, as shown. What is the area, in square inches, of the region that is common to the two triangles? Express your answer in simplest radical form. [asy] draw((0,3)--(0,8)--(4,11)--(8,8)--(8,3)--(4,0)--cycle,black+linewidth(1)); draw((4,0)--(0,8)--(8,8)--cycle, black+dashed+linewidth(1)); draw((0,3)--(4,11)--(8,3)--cycle, black+dotted+linewidth(1)); label("4",(8,5.5),E); [/asy]
Plain-text mathematical notation (without MathML)
By joining alternate vertices of a regular hexagon with edges 4 inches long, two equilateral triangles are formed, as shown. What is the area, in square inches, of the region that is common to the two triangles? Express your answer in simplest radical form. [asy]
draw((0,3)--(0,8)--(4,11)--(8,8)--(8,3)--(4,0)--cycle,black+linewidth(1));
draw((4,0)--(0,8)--(8,8)--cycle, black+dashed+linewidth(1));
draw((0,3)--(4,11)--(8,3)--cycle, black+dotted+linewidth(1));
label("4",(8,5.5),E);
[/asy]
Original LaTeX notation
By joining alternate vertices of a regular hexagon with edges $4$ inches long, two equilateral triangles are formed, as shown. What is the area, in square inches, of the region that is common to the two triangles? Express your answer in simplest radical form. [asy]
draw((0,3)--(0,8)--(4,11)--(8,8)--(8,3)--(4,0)--cycle,black+linewidth(1));
draw((4,0)--(0,8)--(8,8)--cycle, black+dashed+linewidth(1));
draw((0,3)--(4,11)--(8,3)--cycle, black+dotted+linewidth(1));
label("4",(8,5.5),E);
[/asy]

level

Level 5

type

Geometry

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Source and history

task_id
93c5716a-894d-51ce-b4a0-f5204ac5146e
task_key
geometry--test--93c5716a-894d-51ce-b4a0-f5204ac5146e
task_revision_id
1
config / split
geometry / test

Official source

initial import