For the given figure, we will find its perimeter and area one at a time.
Perimeter
Consider the given figure. We can tell that it is a parallelogram. The perimeter of a parallelogram is calculated by adding its four side lengths.
We are given that one side length of the parallelogram is 12yd, but we are missing the other three measurements. However, the opposite sides of parallelogram are congruent, so we know that the length of the opposite side is also 12yd.
Now, note that one of the sides whose length is missing is a side of the right triangle formed on the left of the diagram.
To find the length c we can use one of the trigonometric ratios, as this segment is a hypotenuse 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 hypotenuse. To do it, we can use the sine ratio.
sin 35^(∘)=4/c
Let's find c by solving the above equation.
Therefore, the hypotenuse of this triangle is approximately 6.9738yd. Since the opposite sides in a parallelogram are congruent, the length of the last side is also 6.9738yd. Note that we rounded the length of this side 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: 12+ 6.9738+ 12+ 6.9738=37.9476
The perimeter of the parallelogram to the nearest hundredth is 37.95yd.
Area
The area of a parallelogram is the product of a base and its corresponding height. We can consider the side whose length is 12yd as the base. However, we need to find the height. To do so, we will again pay close attention to the right triangle formed on the left of the diagram.
To find the length h we can use one of the trigonometric ratios again. Let's write an equation using the definition of tangent.
tan 35^(∘)=4/h
Let's find h by solving the above equation.
Therefore, the height of the parallelogram is approximately 5.7126yd. Note that again, we rounded the length of the height to four decimal places so that the final answer is more exact.
Now that we know that the base is 12yd and that the height is 5.7126yd, we can substitute these values in the formula for the area of a parallelogram.
