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: 

\(\displaystyle area=base\times height\)

The solution is: 

\(\displaystyle area=98\times44=4,312\)

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: 

\(\displaystyle area=base\times height\)
Before applying the formula you must find \(\displaystyle \frac{1}{4}\) of \(\displaystyle 12\). 

\(\displaystyle \frac{1}{4}\times12=\frac{12}{4}=12\div4=3\)

The solution is: 

\(\displaystyle area=12\times 3=36\)

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: 

\(\displaystyle area=base\times height\)

The solution is: 

\(\displaystyle area=8.5\times 6.5=55.25\)

Note: prior to applying the formula, the answer choices require you to be able to convert \(\displaystyle 8\frac{1}{2}\) to \(\displaystyle 8.5\), as well as \(\displaystyle 6\frac{2}{4}\) to \(\displaystyle 6.5\). Or, you could have converted the mixed numbers to improper fractions and then multiplied the two terms:

\(\displaystyle 8\frac{1}{2}=\frac{17}{2}\)

\(\displaystyle 6\frac{2}{4}=\frac{26}{4}=\frac{13}{2}\)

\(\displaystyle \frac{17}{2}\times \frac{13}{2}=\frac{221}{4}=55.25\)

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: 

\(\displaystyle area=base\times height\)

Additionally, this problem requires you to find the area of the interior rectangle. This can be simply found by applying the formula: \(\displaystyle area=length\times width\)

Thus, the solution is: 

\(\displaystyle area=10\times 5=50\)

\(\displaystyle 4\times2=8\)

\(\displaystyle 50-8=42\)

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: 

\(\displaystyle area=base\times height\)
Before applying the formula you must find \(\displaystyle \frac{1}{2}\) of \(\displaystyle 140=\frac{140}{2}=70\). 

The solution is: 

\(\displaystyle area=140\times 70=9,800\)

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

\(\displaystyle 14\times7=98\)

There were two total zeros in the factors, so tack on two zeros to the product: 
\(\displaystyle 9,800\)

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: 

\(\displaystyle area=base\times height\)

The solution is: 

\(\displaystyle area=15\times 19=285\)

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: 

\(\displaystyle area=base\times height\)
Before applying the formula you must find \(\displaystyle \frac{1}{3}\) of \(\displaystyle 180=\frac{180}{3}=60\). 

The solution is: 

\(\displaystyle area=180\times 60=10,800\)

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

\(\displaystyle 18\times6=108\)

There were two total zeros in the factors, so tack on two zeros to the product: 
\(\displaystyle 10,800\)

The area of a triangle is \(\displaystyle \frac{1}{2}bh;b:base,h:height\)

Consider the rectangle ABCD

As a rectangle:

\(\displaystyle \overline{AB}=\overline{DC}\)

\(\displaystyle \overline{AD}=\overline{BC}\)

With \(\displaystyle E\) appearing directly in the center of the rectangle.

The area of \(\displaystyle AEB=\frac{1}{2}(\overline{AB})(\frac{1}{2}\overline{BC})=\frac{1}{4}(\overline{AB})(\overline{BC})\)

Notice that the \(\displaystyle \frac{1}{2}\overline{BC}\) term corresponds to the triangle's height.

The area of \(\displaystyle BEC=\frac{1}{2}(\overline{BC})(\frac{1}{2}\overline{AB})=\frac{1}{4}(\overline{BC})(\overline{AB})\)

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.