Explanation The sides of a square are congruent. If the perimeter is 80, each side must be 80/4 = 20.  If each side is 20, the area is base times height = 20 * 20 = 400.

Explanation The diagonals of a rhombus bisect each other and are perpendicular. You see 4 right triangles in the center of the rhombus with sides of 5 and 12 .  Using the Pythagorean Thm, the third side of each triangle is 13.  So the perimeter is 4(13)=52.

Explanation The square has 4 congruent sides. Each side must be 6. The diagonal makes two right triangles. Use the Pyth. Thm to find the diagonal.

Explanation The opposite sides of a parallelogram are equal. 2x+10 = 5x - 20  (solve for x) x=10.  Now substitute 10 into the side you are looking to find, 4x - 1.   Answer is 40 - 1 = 39.

Explanation The opposite angles of a parallelogram are =. The consecutive angle are supplementary. There is one other angle of 60 and the remaining two angles are supplements of 60. (Supplementary means add to 180.)

Explanation Angles A and B are consecutive and are supp. Ratios are expressed with x's, therefore 2x + 7x = 180. Solving for x gives x = 20. Remember to find angle A.  2(20) = 40

Explanation All sides of a rhombus are equal. Set y+8=4y-7  and solve for y. y= 5, but remember to solve for MA.

Explanation In a rectangle the diagonals are equal and bisect each other.  So all 4 sections of the diagonals =20. 3x+y=20   and    4x-2y=20 Solve these simultaneous equations. Multiple every term in 3x+y=20 by 2.  (6x+2y=40) When you add the equations, the y terms will cancel out.  This gives x = 6. Substitution gives y = 2.

Explanation The median is one-half the sum of the bases. 25 = (1/2) * (x + 40) 25 = 0.5 (x + 40) 50 = x + 40 x = 10

Explanation Perimeter is the distance around the outside. A quadrilateral has 4 sides. Add all of the sides and set them equal to 49. When you solve for x, the value is 6. The side represented by x is also the smallest side.