M3 Review - Geometry (non - circles)

In triangle MNO, point Q is the circumcenter and point P is the midpoint of side MN. If

• MN = 24 units

• QP = 5 units

• QM = (5x – 2) units

what is the value of x? Type your numeric answer in the space provided.

(a)  

A triangle has points K(4, 7), L(6, 1), and M(0, 3) and has uniform density. What is the approximate distance between point K and the center of gravity for the triangle?

In triangle ABC shown, point D is the midpoint of side AB and point E is the midpoint of side BC.

What is the length of segment DE?

Type your numeric answer in the space provided.

(a)  

Rectangle DEFG has diagonals DF and EG that intersect at point K.

EG = (7x – 12) cm

KF = (2x + 9) cm

What is the value of x?

Type your numeric answer in the blank space.

(a)  

In the rectangle WXYZ shown, WY = (3x – 8) ft  and ZX = (2x + 5) ft. What is the length of segment ZM?

In Rhombus ABCD, the length of diagonal AC = 20 inches and the length of diagonal BD = 12 inches.

What is the approximate perimeter of rhombus ABCD?

A regular hexagon has a perimeter of 48 inches.

What is its approximate area?

An area rug is to be made in the shape of a regular hexagon with a side length of 6 feet. The rug costs $500. How much does the rug cost per square foot?

A cylinder has a height of (3x + 4) and a radius of (x - 2). Which expression represents the volume of the cylinder?

An open-top box is formed by cutting out equal squares of side length x from each corner of a 12 inch by 15 inch rectangular piece of cardboard.

What is the maximum volume the box can hold?