A parallelogram must have two sets of opposite sides that are congruent/parallel. However, to find the area of a paralleogram, you need to know the base and height lengths. Since this problem provides both the base and height measurements, apply the formula: 



Additionally, this problem requires you to find the area of the interior rectangle. This can be simply found by applying the formula: 

Thus, the solution is: 

By definition a parallelogram has two sets of opposite sides that are congruent/parallel. However, to find the area of a paralleogram, you need to know the base and height lengths. Since this problem provides both the base and height measurements, apply the formula: 


Before applying the formula you must find  of . 

The solution is: 



Note: when working with multiples of ten remove zeros and then tack back onto the product.



There were two total zeros in the factors, so tack on two zeros to the product: 

A parallelogram must have two sets of opposite sides that are congruent/parallel. However, to find the area of a paralleogram, you need to know the base and height lengths. Since this problem provides both the base and height measurements, apply the formula: 



The solution is: 

By definition a parallelogram has two sets of opposite sides that are congruent/parallel. However, to find the area of a paralleogram, you need to know the base and height lengths. Since this problem provides both the base and height measurements, apply the formula: 


Before applying the formula you must find  of . 

The solution is: 



Note: when working with multiples of ten remove zeros and then tack back onto the product.



There were two total zeros in the factors, so tack on two zeros to the product: 

The area of a triangle is 

Consider the rectangle ABCD

As a rectangle:

With  appearing directly in the center of the rectangle.

The area of 

Notice that the  term corresponds to the triangle's height.

The area of 

The two quantities are equal.

There are two components to solving this geometry puzzle. First, one must be aware that the sum of the measures of the interior angles of a parallelogram is 360 degrees (sum of the interior angles of a figure = 180(n-2), where n is the number of sides of the figure). Second, one must know that the other two interior angles are doubles of those given here. Thus if we assign one interior angle as x and the other as x-25, we find that x + x + (x-25) + (x-25) = 360. Combining like terms leads to the equation 4x-50=360. Solving for x we find that x = 410/4, 102.5, or approximately 103 degrees. Since x is the measure of the larger angle, this is our answer.

By using the properties of parallelograms along with those of supplementary angles, we can rewrite our figure as follows:

Recall, for example, that angle  is equal to:

, hence 

Now, you know that these angles can all be added up to . You should also know that 

Therefore, you can write:

Simplifying, you get:

Now, this means that:

 and . Thus, the two values are equal.

Because of the character of parallelograms, we know that our figure can be redrawn as follows:

Because it is a four-sided figure, we know that the sum of the angles must be . Thus, we know:

Solving for , we get:

In this problem, you are told that the sum of the two bases in a parallelogram is  Since the two bases must be equivalent, each side must equal: . Additionally, the problem states that the adjacent sides are  the length of the bases. Therefore, an adjacent side to the base must equal: