# Review of Geometry II

### Review Test

What is the perimeter of a pentagon whose side lengths are 3, 5, 7, 2, and 13?

A line segment of length 4 is bisected by a line segment of length 12. What is the perimeter of this figure?

If a circle is inscribed in an equilateral triangle with side length 6, what is the circumference of that circle?

A circle with what radius has the same area as circumference?

In parallelogram ABCD, AB has length 2 BC has length 6, and angle A is 30 degrees. What is the area of parallelogram ABCD?

What is the area of the figure below?

What is the area of the shaded region?

What must be the side length of an equilateral triangle in order for its area to equal its perimeter?

What is the area of a regular hexagon with side length 6?

Two parallel chords of length 2 cut a circle into 4 congruent arcs. What is the area of this circle?

What is the area of a triangle with sides of lengths 5, 6, and 7?

What is the area of a triangle with side lengths of 9, 40, and 41?

If a circle with area 49 is inscribed in a square, what is the area of that square?

What is the surface area of a right pyramid whose base is a square with side length 6, and whose altitude has length 4?

What is the surface area of a sphere with radius 4?

The volume of a right circular cone is 180Π . What is the volume of the right circular cone that shares a base with the right circular cylinder and whose vertex lies at the center of the other base of the cylinder?

The volume of a prism is 240, and its base has area 12. What are the lengths of its lateral faces?

A prism has a rhombus for a base. The length of the sides of the rhombus is 13, and the longer diagonal of the rhombus is 24. The altitude of the prism is 12. What is its volume?

A sphere is circumscribed about a cube with edge length 5 . What is the volume of the sphere

If the lengths of a triangle are 16, 30, and 34, what is its most specific classification?

What do you know about an isosceles triangle if it contains a 60 degree angle?

What are the lengths of the sides of an isosceles right triangle?

A triangle is formed by a diameter of a circle and two chords of that circle. The radius of the circle has length x . One of the sides of the triangle has length x . The area of the triangle is 32 . What are the lengths of the three sides of the triangle?

When two equilateral triangles are joined by one side, what new polygon is formed?

A triangle's base is three, and its area is 6. What kind of triangle is it?

An isosceles triangle with base 8 is divided into two triangles by the altitude from its vertex angle. If the altitude of the isosceles triangle was 7.5, what were the lengths of its legs?

An isosceles triangle has an angle of 110 degrees. Which angle is it?

If triangle ABC is congruent to triangle DEF, which of the following are true?

Which kinds of triangles always have six parts that correspond?

The diagonals of square ABCD intersect at point E. Which of the following pairs of triangles are congruent?

Triangles ABC and DEF are both right triangles, with their right angle at vertex A and D, respectively. Which of the followiong statements is true?

Triangle ABC has side lengths 9, 10, and 11. Triangle DEF has side lengths x , x + 1 , and x + 2 . If the two triangles are similar, what is the value of x ?

What kinds of triangles are always similar?

Two right triangles have equal hypotenuses. What is true of these triangles?

Find the value of x .

A circle segment is defined by a chord that cuts an arc of 60 degrees. The radius of the circle is 6. What is the area of the sector that is bound by the same arc?

What is the area of triangle ABC?

An angle has its vertex inside a cirlce. When its sides are extended into lines, they intercept two arcs, one of 30 degrees, and another of 210 degrees. What is the measure of the supplement of the original angle?

An isosceles trapezoid has legs of length 2 and upper base angles with measure 120 degrees. What is the area of such a trapezoid if its bases sum to 24?

In an equilateral triangle, which of the following are true?

What is the measure of angle 1?

Find the value of x .

If the circumcircle of a triangle is contained by one of its sides, what kind of triangle is it?

A regular hexagon has side length 2. A triangle is formed by an apothem, a radius, and part of a side, that part which lies between the endpoint of the apothem and the vertex to which the radius is drawn. What are the lengths of the sides of this triangle?

If a tangent segment of length is drawn from a fixed point outside a circle with radius one, what is the length of the segment with an endpoint at the center of the circle and at the fixed exterior point?

What is true of a point that is equidistant from all three vertices of a triangle?

What is the measure of angle A?

What figure results from an isosceles trapezoid whose legs are extended until they intersect? (Give the most specific term possible)

What is the measure of angle x ?

Which of the following are determined by three noncolinear points?