Find the area of the parallelogram.( with base(s)=10 and the side length(s)=6cm. I don't know the height or area so how do I get my answer? here are the multiple choice answers.
a.)15√3 cm^2
b.)15√2 cm^2
c.) 30√3 cm^2
not enough information
a parallelogram with base 10 and other side 6 is not unique, I can draw more than one with those dimensions.
Perhaps an angle was given?
To find the area of a parallelogram, you need to know either the base and the height or the lengths of both the bases. In this case, you are given one base length (10 cm) and one side length (6 cm). However, since the side length is not the same as the height, we cannot directly calculate the area using this information.
To proceed, we need to use the fact that the opposite sides of a parallelogram are equal in length. Since one side length is 6 cm, it means the opposite side is also 6 cm.
Now, draw a perpendicular from the side of length 6 cm to the base. This perpendicular line segment represents the height of the parallelogram. Using the properties of right-angled triangles, we can calculate the height.
A right-angled triangle is formed with the base (10 cm), height (which we need to find), and the side (6 cm). Using Pythagoras' theorem, we can find the height.
Let h be the height.
According to Pythagoras' theorem: h^2 = 6^2 - (10/2)^2
Simplifying: h^2 = 36 - 25 = 11
Taking the square root: h = √11 cm
Now that we have the height (√11 cm), we can calculate the area of the parallelogram using the formula: Area = base × height.
Area = 10 cm × √11 cm ≈ 10√11 cm^2
Comparing the options given, we can see that the closest answer is c.) 30√3 cm^2. However, the exact value of the area is approximately 10√11 cm^2.