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Geometric Modeling in Two Dimensions — Test Answers

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1
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What type of polygon is shown?

A
convex hexagon
B
concave hexagon
C
convex heptagon
D
concave heptagon
2
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Figure ABCD is a parallelogram. Two trapezoids are created using line segment XY such that line segment AX is congruent to line segment CY What is true about the areas of the trapezoids?

A
Each area is equal to half of the area of ABCD .
B
Each area is equal to the area of ABCD .
C
The area of AXYD is less than the area of BXYC .
D
The area of AXYD is greater than the area of BXYC .
4

A section of a rectangle is shaded. The area of the shaded section is 63 square units. What is the value of x ?

A
21 units
B
9 units
C
18 units
D
11 units
5

What is the total area of the three triangles?

A
13 point 5 square units
B
14 square units
C
12 point 5 square units
D
13 square units
6

What is the measure of the radius, c , rounded to the nearest inch? Use the appropriate trigonometric ratio to solve.

A
6 in.
B
14 in.
C
10 in.
D
24 in.
7

What is the area of triangle LMN ?

A
14 square units
B
12 square units
C
24 square units
D
15 square units
8

What is the area of the composite figure?

A
268 square centimeter
B
262 square centimeter
C
266 square centimeter
D
264 square centimeter
9

Which polygon is a concave octagon?

A
Image with description A polygon with 8 sides and no interior angles greater than 180 degrees.
B
Image with description A polygon with 8 sides and 1 interior angle greater than 180 degrees.
C
Image with description A polygon with 8 sides and no interior angles greater than 180 degrees.
D
Image with description A polygon with 7 sides and 1 interior angle greater than 180 degrees.
10

How does the area of triangle ABC compare to the area of parallelogram GHJK ?

A
The area of triangle ABC is 2 square units greater than the area of parallelogram GHJK .
B
The area of triangle ABC is 1 square unit less than the area of parallelogram GHJK .
C
The area of triangle ABC is 1 square unit greater than the area of parallelogram GHJK .
D
The area of triangle ABC is equal to the area of parallelogram GHJK .
11

What is the area of the shaded region?

A
25 pi minus 48 times square centimeter
B
25 pi minus 24 times times square centimeter
C
25 pi minus 12 times square centimeter
D
25 pi minus 30 times square centimeter
12

What is the perimeter?

A
5 centimeters
B
20 centimeters
C
10 centimeters
D
2 centimeters
13

What is the area of parallelogram RSTU ?

A
28 square units
B
24 square units
C
32 square units
D
21 square units
14

How can you decompose the composite figure to determine its area?

A
as a triangle, a rectangle, and a semicircle
B
as two triangles, a rectangle, and a circle
C
as three triangles and a circle
D
as a triangle, a pentagon, and a semicircle
15

Recall that in a 30 degrees - 60 degrees - 90 degrees triangle, if the shortest leg measures x units, then the longer leg measures x square root of 3 units and the hypotenuse measures 2 x units.

A
300 minus 75 pi square feet
B
150 square root of 3 minus 75 pi times square feet
C
150 square root of 3 minus 25 pi square feet
D
300 minus 25 pi square feet

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