Area of Triangles and Parallelograms — Unit test Answers

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.

Henry and Liani have 200 feet of wood to frame a flower bed. Henry wants the bed to be a square, while Liani wants it to be a rectangle with dimensions of 55 feet and 45 feet.Which statement is true regarding the areas of the two flower beds?

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 oblique prism has a square base and height of 3 centimeters.

The table shows information about Town A in Illinois and Town B in Florida.

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?

To find the area of parallelogram RSTU, Juan starts by drawing a rectangle around it. Each vertex of parallelogram RSTU is on a side of the rectangle he draws.

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

A county in North Carolina spans 532 square miles. The population density of deer in the county is 11 deer per square mile.How many deer live in the county? Round to the nearest whole number, if necessary.

The height of a right rectangular prism is 3 units greater than the length of the base. The edge length of the square base is x units.Which expression represents the volume of the prism, in cubic units?

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

A right prism has a rhombus as a base. The height of the prism is 6 inches and the volume is 144 cubic inches.Which could be the lengths of the diagonals of the rhombus?

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).

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.