Question

What percent of the total area of the rectangle is colored?

Answer 1

Hint: In the given question, we are required to find the percentage of the total area of the rectangle that is shaded in the figure given to us. In such types of questions, the knowledge of concepts of fractions and percentages will be much needed and essential. Also, prerequisite knowledge of properties of the rectangle related to its area will be of significant use for solving such problems.

Complete step by step solution:
In the given problem, a figure is given to us. The figure consists of a rectangle, a portion of which is shaded. We have to find the percentage of the total area of the rectangle that is shaded in the given figure.
The rectangle is divided into four congruent triangles by joining the two diagonals of the rectangle.
We know that area of a rectangle is computed with the help of formula ${\text{Area}}\,{\text{of}}\,{\text{Rectangle}} = {\text{Length}} \times {\text{Breadth}}$ and area of a triangle is computed with help of formula ${\text{Area}}\,{\text{of}}\,{\text{Triangle}} = \left( {\dfrac{1}{2}} \right) \times {\text{Base}} \times {\text{Height}}$.
So, area of the given rectangle \[ = {\text{L}} \times {\text{W = LW}}\]
Base of the triangle that is shaded is \[{\text{L}}\] and height is \[\left( {\dfrac{{\text{W}}}{2}} \right)\] .
So, area of the shaded triangle \[ = \left( {\dfrac{1}{2}} \right) \times {\text{L}} \times \left( {\dfrac{{\text{W}}}{2}} \right) = \dfrac{{{\text{LW}}}}{4}\]
Percentage of the total area of the rectangle that is shaded \[ = \dfrac{{\dfrac{{{\text{LW}}}}{4}}}{{{\text{LW}}}} \times 100\% \]
\[ \Rightarrow \dfrac{{100\% }}{4}\]
\[ \Rightarrow 25\% \]
So, the percentage of the total area of the rectangle that is shaded is \[25\% \].

Note: There are various methods of finding the percentage of the shaded portion in the figure given to us. We can also find the percentage of the shaded region by counting the number of triangles that are shaded as the four triangles that are formed by joining the diagonals of the rectangle are congruent to each other. Since only one of the four triangles are shaded, so the percentage of shaded region is \[25\% \].