Question

the figures shown are rectangles. each rectangle represents one whole
which rectangle is shaded to represent $\frac{1}{4}$ the area of the whole?
a figure l
b figure j
c figure k
d figure m

Explanation:

Step1: Analyze Figure J

Assume the area of the rectangle is \(1\). Figure J is divided into \(4\) parts (not equal - area). The shaded part is more than \(\frac{1}{4}\).

Step2: Analyze Figure K

Figure K is divided into \(4\) parts (not equal - area). The shaded part is more than \(\frac{1}{4}\).

Step3: Analyze Figure L

Let the area of the rectangle be \(A\). The rectangle in Figure L is divided into \(4\) equal - area triangles (because the diagonals of a rectangle bisect each other and the area of a triangle \(=\frac{1}{2}\times base\times height\). For the four triangles formed by the diagonals of a rectangle, they have the same base and height). The area of the shaded triangle is \(\frac{1}{4}\) of the area of the rectangle.

Step4: Analyze Figure M

Figure M is divided into \(4\) parts (not equal - area). The shaded part is less than \(\frac{1}{4}\).

Answer:

A. Figure L