Density and Design Problems — Unit test Answers

On a coordinate plane, rhombus W X Y Z has points (negative 3, 1), (1, 4), (5, 1), and (1, negative 2).

Which statements about the octagon are true? Select two options.

Triangle X Y Z is reflected over its hypotenuse to form kite X Y Z Y prime. Hypotenuse X Z has a length of 13, X Y is 5, and Y Z is 12.

On a coordinate plane, 2 parallelograms are shown. Parallelogram 1 has points (0, 2), (2, 6), (6, 4), and (4, 0). Parallelogram 2 has points (2, 0), (4, negative 6), (2, negative 8), and (0, negative 2).

An interior angle of a regular polygon has a measure of 108°. What type of polygon is it?

Galina is finding the area of triangle RST. To do so, she follows the steps in the table.Step 1Draw a rectangle around triangle RST.Step 2Find the area of the rectangle.Step 3Find the area of the three right triangles created by the sides of the rectangle and the intersection with each vertex of the triangle.Step 4Subtract the area of the right triangles from the area of the rectangle.

Complete the steps, which describe how to find the area of the shaded portion of the circle.

On a coordinate plane, rhombus W X Y Z has points (negative 3, 1), (1, 4), (5, 1), and (1, negative 2).

A regular hexagon is shown.

Which polygon is a convex heptagon?

Parallelogram A B C D is shown. Line segment X Y goes from point X on side A B to point Y on side C D to form 2 trapezoids. The length of X Y is 11 and the length of Y C is 4. Sides X B and C Y are congruent.

A semicircle with diameter 8 inches is connected to a triangle with a base length of 8 inches. The height of the triangle is 3 inches.

A regular heptagon has a radius of approximately 27.87 cm and the length of each side is 24.18 cm.What is the approximate area of the heptagon rounded to the nearest whole number? Recall that a heptagon is a polygon with 7 sides.

On a coordinate plane, triangle R S T has points (negative 3, 2), (3, 2), and (negative 1, 1). An altitude is drawn from point T to point U at (negative 1, 2).

The more people living in an area, the more likely it is that public buses will be used. City A has a population of 51,242 and covers an area of 89.22 mi2. City B has a population of 50,178 and covers an area of 8.12 mi2.Which statement about use of public buses in the cities is most likely true?