Topic 4 · Test

Unit 4 test: Geometry

15 questions. Answer them all, then submit to see your score. Solutions unlock after you submit.

This mock contest covers the whole Geometry unit: angles and polygons, triangles and the Pythagorean theorem, area of polygons, circles, volume and surface area, coordinate geometry, and similar figures.

Question 1

Each interior angle of a regular polygon measures $140^\circ$ . How many sides does the polygon have?

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 2

One exterior angle of a triangle measures $130^\circ$ . One of the two interior angles not next to it measures $55^\circ$ . What is the measure of the other one?

Question 3

A rectangle measures $20$ by $21$ . How long is its diagonal?

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 4

What is the area of a triangle with side lengths $17$ , $17$ and $16$ ?

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 5

An isosceles right triangle has a hypotenuse of length $10$ . What is its area?

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 6

A rhombus has side length $17$ , and one of its diagonals has length $30$ . What is the area of the rhombus?

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 7

Triangle $ABC$ has area $90$ . Point $D$ is on $BC$ with $BD = 2 \cdot DC$ , and $E$ is the midpoint of $AD$ . What is the area of triangle $ABE$ ?

Question 8

A sector of a circle has radius $12$ and a central angle of $60^\circ$ . What is its area? Express your answer in terms of $\pi$ .

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 9

Two circles have the same center. A chord of the larger circle has length $16$ and is tangent to the smaller circle. What is the area of the region between the two circles? Express your answer in terms of $\pi$ .

A chord of the large circle, tangent to the small circle. Radii to the tangent point and to the end of the chord form a right triangle.

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 10

A cube has surface area $294$ square inches. What is its volume, in cubic inches?

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 11

A cone with radius $6$ inches and height $9$ inches is filled with water. The water is poured into an empty cylinder that also has radius $6$ inches. How deep is the water in the cylinder, in inches?

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 12

What is the area of the triangle with vertices $(2, 1)$ , $(8, 4)$ and $(4, 7)$ ?

The triangle with vertices (2, 1), (8, 4) and (4, 7).Open in grapher →

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 13

At what point do the lines $y = 2x + 1$ and $y = -x + 10$ intersect? Give your answer as an ordered pair.

Enter a point like (2, -3)

Question 14

In triangle $ABC$ , $D$ is on $AB$ and $E$ is on $AC$ with $\overline{DE} \parallel \overline{BC}$ . If $AD = 3$ , $DB = 5$ and $BC = 12$ , what is $DE$ ?

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 15

Two similar pyramids have volumes $8$ and $27$ . What is the ratio of their surface areas?