SAT Practice Test - Math - Important Points of Triangles

SAT practice tests arranged by topic and difficulty level. In this section find tips and tactics for solving questions that focus on Important Points of Triangles.

Learn about Important Points of Triangles

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SAT Practice Test - Math - Data Interpretation from Tables

SAT practice tests arranged by topic and difficulty level. In this section find tips and tactics for solving SAT questions that focus on Data Interpretation from Tables.

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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