The perimeter of a rectangle is calculated by adding the lengths of its four sides. The area of a rectangle is calculated by multiplying its length and width.
Perimeter: 9.19in. Area: 4.79in.^2
Practice makes perfect
For the given figure, we will find its perimeter and area one at a time.
Perimeter
Consider the given figure.
We are given that the length of one of the sides is 3 inches and we know that the opposite side is congruent, so it also measures 3 inches. We know that the remaining sides are congruent to each other, so we need to find just one of the remaining side lengths. To do so, we will pay close attention to the right triangle formed by the diagonal and two sides of the figure.
To find the length w we can use one of the trigonometric ratios, as this segment is a leg of a right triangle. We know the length of one of the legs of this triangle and the measure of the angle opposite this leg. We want to find the measure of the other leg, w. To do it, we can use the tangent ratio.
tan 62^(∘)=3/w
Let's find w by solving the above equation.
Therefore, the length of the two remaining sides is approximately 1.5951 inches. Note that we rounded the length of the height to four decimal places so that the final answer is more exact.
Now we can add the four side lengths to obtain the perimeter.
Perimeter: 3+ 1.5951+ 3+ 1.5951=9.1902
The perimeter of the rectangle to the nearest hundredth is 9.19in.
Area
The given figure is a parallelogram with four right angles. Therefore, it is a rectangle. To find its area, we need to multiply the length by the width. In our case the length is 3 and the width is 1.5951.
