Since  is acute, a right triangle can be constructed with an altitude as one leg and a side as the hypotenuse, as is shown here. The height of the triangle must be less than its sidelength of 8 inches.

The height of the parallelogram must be less than its sidelength of 8 inches.

The area of the parallelogram is the product of the base and the height - which is 

 Therefore, 

(B) is greater.

The area of a parallelogram is the product of its height and its base; its slant length is irrelevant. Both parallelograms have the same height (8 inches) and the same base (1 foot, or 12 inches), so they have the same areas.

A rhombus, by definition, has four sides of equal length. Therefore, . Also, since  and  are the midpoints of their respective sides, 

We will assign  to the common length of the four half-sides of the rhombus.

Also, both  and  are altitudes of the rhombus; the are congruent, and we will call their common length  (height).

The figure, with the lengths, is below.

Rectangle  has dimensions  and ; its area, 150, is the product of these dimensions, so

The area of the entire Rhombus  is the product of its height  and the length of a base , so

.

The measure of  is actually irrelevant. The perimeter of the parallelogram is the sum of its four sides; since opposite sides of a parallelogram have the same length, the perimeter is

 inches, 

making the quantities equal.

The perimeter of a parallelogram is the sum of its sidelengths; its height is irrelevant. Also, opposite sides of a parallelogram are congruent.

The perimeter of parallelogram A is 

 inches;

The perimeter of parallelogram B is 

 inches.

(A) is greater.

All four sides of a rhombus have the same length, so we can find the perimeter of Rhombus  by taking the length of one side and multiplying it by four. Since , the perimeter is four times this, or .

Note that the length of  is actually irrelevant to the problem.

In Parallelogram , and  are adjoining sides; there is no specific rule for the relationship between their lengths. Therefore, no conclusion can be drawn of and , and no conclusion can be drawn of the relationship between and .

Opposite angles of a parallelogram must have the same measure, so the correct choice must have two pairs, each of the same angle measure. We can therefore eliminate  and  as choices. 

Also, the sum of the measures of the angles of any quadrilateral must be , so we add the angle measures of the remaining choices:

: 

, so we can eliminate this choice.

:

, so we can eliminate this choice.

; this is the correct choice.

The sum of two consecutive angles of a parallelogram is .

157 is the correct choice.

In Parallelogram , and are opposite angles and are therefore congruent. This means that

Both are positive, so .