SAT Practice Test - Math - Convex Polygons

SAT practice tests arranged by topic and difficulty level. In this section find tips and tactics for solving SAT questions that focus on Convex Polygons.

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SAT Practice Test 2015.

The figure above shows a regular hexagon with sides of length a and a square with sides of length a. If the area of the hexagon is $384\sqrt{3}$ square inches, what is the area, in square inches, of the square?

A) 256
B) 192
C) $64\sqrt{3}$
D) $16\sqrt{3}$

Answer:

The area of an equilateral triangle is given by the formula $A_T=L^2\sqrt{3}/4$, where L is the length of the side of the triangle.

The hexagon is composed by 6 equilateral triangles. Therefore the area of the hexagon is given by the formula $A_H=6(A_T)=6L^2\sqrt{3}/4$.

And it was given that the area of the hexagon is $384\sqrt{3}$. Thus
$6L^2\sqrt{3}/4=384\sqrt{3}$
$6L^2/4=384$
$L^2=384(4)/6$
$L^2=256$. This is the area of the square.

Answer: A

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SAT Practice Test 2015. $nA=360$
The measure A, in degrees, of an exterior angle of a regular polygon is related to the number of sides, n, of the polygon by the formula above. If the measure of an exterior angle of a regular polygon is greater than 50°, what is the greatest number of sides it can have?
A) 5
B) 6
C) 7
D) 8

Answer:

$nA=360$
$A=360/n$

Since A>50,
$360/n>50$
$360>50n$
$360/50>n$
$7,2>n$

Answer: C

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