a certain city block is in the form off parallelogram. two of it's side are each 225 meters long, the other two sides are each 145 meters long. if the distance between the first two pair is 80 meters. find the area of the land in the block and the length of the diagonals.
the area, of course, is base * height = 225*80 = 18000m^2
Use the law of cosines for the diagonals. The angles between the sides are θ and π-θ, where
sinθ = 80/145
a certain city block is in the form of parallelogram .Two of.its parallel sides are each 130 meters long ;the other two sides are each 70 meters in length .if the distance between the first two parallel sides is 40 meters,find the area of a lot and the length of the diagonals
Well, well, a parallelogram city block! How exciting! Let's get down to business and solve this puzzle, shall we?
To find the area of the land in the block, we can use the formula: Area = base × height. Since the base of the parallelogram is 225 meters and the height is given as 80 meters, we can plug these values in: Area = 225 × 80.
Area = 18,000 square meters.
Ta-da! Now, let's move on to the length of the diagonals. In a parallelogram, the diagonals are usually not equal, but they have the same length. So let's calculate one of them first.
Using the Pythagorean theorem, we can find the length of one of the diagonals (let's call it d) with the given side lengths of 225 meters and 145 meters, and the distance between the two pairs of sides (80 meters).
d² = (225² + 145²) - 2(225)(145)cos(theta).
Now, the tough part is finding the angle theta (θ). Without that, we can't proceed with calculating the diagonal length. So, unless you can provide the angle, I won't be able to give you the exact length of the diagonals. But don't worry, I'm here to make you smile, even if I can't solve this paradox!
To find the area of the land in the block, we can use the formula for the area of a parallelogram, which is given by:
Area = base × height
In this case, the base of the parallelogram is 225 meters and the height is 80 meters. So we can calculate the area as:
Area = 225 meters × 80 meters = 18,000 square meters
Therefore, the area of the land in the block is 18,000 square meters.
To find the length of the diagonals of the parallelogram, we can use the Pythagorean theorem. The diagonals of a parallelogram bisect each other, so we can treat each side of the parallelogram as the hypotenuse of a right triangle.
Let's call the first diagonal d1 and the second diagonal d2.
Applying the Pythagorean theorem, we have:
d1² = (145 meters)² + (80 meters)²
d2² = (225 meters)² + (80 meters)²
Calculating these values:
d1² = 21025 meters² + 6400 meters² = 27425 meters²
d2² = 50625 meters² + 6400 meters² = 57025 meters²
Now, taking the square root of both sides to find the lengths of the diagonals:
d1 ≈ √27425 meters ≈ 165.7 meters (rounded to one decimal place)
d2 ≈ √57025 meters ≈ 238.9 meters (rounded to one decimal place)
Therefore, the lengths of the diagonals of the parallelogram are approximately 165.7 meters and 238.9 meters.
To find the area of the land in the block, we can use the formula for the area of a parallelogram: A = base × height. In this case, the base of the parallelogram is the distance between the first two pairs of sides, which is given as 80 meters. The height is one of the sides of the parallelogram that is perpendicular to the base and is given as 145 meters.
Therefore, the area of the land in the block is A = 80 meters × 145 meters = 11,600 square meters.
To find the length of the diagonals, we can use the Pythagorean theorem. In a parallelogram, the diagonals bisect each other and are equal in length.
Let's call the length of the diagonals as D. We can express D in terms of the given side lengths using the Pythagorean theorem:
D^2 = (225 meters)^2 + (145 meters)^2
D^2 = 50,625 square meters + 21,025 square meters
D^2 = 71,650 square meters
Taking the square root of both sides:
D = √(71,650) meters
D ≈ 267.96 meters
Therefore, the length of the diagonals in the parallelogram is approximately 267.96 meters.