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Geometry and Measurement

SAT Polygons

         

What is the sum of the measures of the angles of a convex polygon with \(11\) sides?

(A) \(\ \ 810\)
(B) \(\ \ 1440\)
(C) \(\ \ 1620\)
(D) \(\ \ 1800\)
(E) \(\ \ 1980\)

\(\)

A botanical garden is divided into regular hexagons, as shown in the figure above. A fence is constructed which surrounds the garden. If the side of each hexagonal section is \(10\) feet long, which of the following is the shortest possible length of the fence in yards? (3 ft = 1 yd)

(A) \(\ \ 60\)
(B) \(\ \ 80\)
(C) \(\ \ 180\)
(D) \(\ \ 240\)
(E) \(\ \ 480\)

\(\)

In the figure above, \(A =45, B = 79,\) and \(C=15.\) For what values of \(x\) and \(y\) will the quadrilateral above be a parallelogram?

(A) \(\ \ x=3, y=8\)
(B) \(\ \ x=8, y=3\)
(C) \(\ \ x=15, y = 15\)
(D) \(\ \ x=15, y=8\)
(E) \(\ \ x=15, y = 64\)

A rectangle and a square both have perimeters equal to \(24.\) If the width of the rectangle is \(3,\) what is sum of their areas?

(A) \(\ \ 9\)
(B) \(\ \ 27\)
(C) \(\ \ 36\)
(D) \(\ \ 63\)
(E) \(\ \ 99\)

\(\)

Shown above are three squares. If \(a=3,\) what is the area of the unshaded region in the diagram above?

(A) \(\ \ 90\)
(B) \(\ \ 99\)
(C) \(\ \ 117\)
(D) \(\ \ 144\)
(E) \(\ \ 189\)

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