The lengths of two sides of a parallelogram are 7.4cm and 9.2cm and one of the diagonals has a length of 6.2 cm. Find the area of the parallelogram.
Oh, di-di-di-diagonal dilemma! Don't get too parallelo-distressed, my friend! To find the area of a parallelogram, we can use the formula: area = base × height. But wait, we don't have the height! No worries, let's call it 'h' (you know, because 'height' starts with an 'h').
Since the two sides of the parallelogram are adjacent and form the base, we know that the base is 7.4 cm. Now, let's focus on finding the height. Feeling a bit figurative today? Let's turn the diagonal into a height by using the formula: height = (2 × area) / base.
But hey, we still don't know the area! Can't blame me for trying to avoid math, right? Since we're working with a parallelogram, we know that the diagonals bisect each other, forming four right-angled triangles. So, let's use Pythagoras to find the height of one of those triangles! We have the hypotenuse (6.2 cm) and the base (4.6 cm), so we can calculate the height using this trusty formula: height^2 = hypotenuse^2 - base^2.
Now that we've found the height, we can substitute it into our first formula to find the area: area = base × height. Calculate that, and voila! You've got the area of the parallelogram. Remember, math can be a real jester sometimes, but don't let it scare you off.
To find the area of a parallelogram, you need to know the length of the base and the height.
In this case, the two sides of the parallelogram given (7.4 cm and 9.2 cm) can be considered as the base and the height.
The area of a parallelogram can be calculated using the formula:
Area = base x height
Let's calculate the area using the given dimensions:
Base = 7.4 cm
Height = 9.2 cm
Area = 7.4 cm x 9.2 cm
= 67.68 cm²
Therefore, the area of the parallelogram is 67.68 square centimeters.
To find the area of a parallelogram, we can use the formula A = base × height, where the base is the length of one of the sides and the height is the length of the corresponding altitude.
First, let's determine the height of the parallelogram using the given lengths of the two sides and the length of one of the diagonals.
We know that the diagonals of a parallelogram bisect each other, meaning they divide each other into two equal parts.
Let's denote the length of the diagonals as d1 and d2, and the lengths of the sides as a and b.
In this case, the lengths of the sides are a = 7.4 cm and b = 9.2 cm, and the length of one of the diagonals is d1 = 6.2 cm.
Since the diagonals bisect each other, we can find the length of the other half of the diagonal (d2) using the formula:
d2 = 2 × d1 - a
Substituting the values we know:
d2 = 2 × 6.2 cm - 7.4 cm = 5 cm
Now that we have the lengths of the sides and the height of the parallelogram, we can calculate the area using the formula:
A = base × height = a × b
Substituting the values we know:
A = 7.4 cm × 5 cm = 37 cm^2
Therefore, the area of the parallelogram is 37 square centimeters.
get the angle θ between the sides using the law of cosines.
area = 9.2*7.4 sinθ