Question

instructions
choose the best answer. if necessary, use the paper you were given.
question
in the large square above, what is the area of the shaded region?
$\frac{3}{4}$
1
$1\frac{1}{4}$
$1\frac{1}{2}$

Explanation:

Step1: Analyze the shape of the shaded region

The shaded region is a parallelogram. The base of the parallelogram is \(1\) (since the side - length of each small square - like part is \(1\)) and the height is \(1.5\).

Step2: Use the formula for the area of a parallelogram

The formula for the area of a parallelogram is \(A = b\times h\), where \(b\) is the base and \(h\) is the height. Substituting \(b = 1\) and \(h=\frac{3}{2}\) (because \(1 + 0.5=1.5=\frac{3}{2}\)), we get \(A=1\times\frac{3}{2}=\frac{3}{2}=1\frac{1}{2}\).

Another way:

Step1: Use the property of congruent shapes

We can also use the fact that the area of the shaded region is equal to the area of a rectangle with length \(1\) and width \(1.5\) (by moving the non - shaded parts around).

Step2: Calculate the area

Using the formula \(A = l\times w\) (where \(l\) is length and \(w\) is width), with \(l = 1\) and \(w=\frac{3}{2}\), we have \(A=1\times\frac{3}{2}=\frac{3}{2}=1\frac{1}{2}\)

Answer:

\(1\frac{1}{2}\)