A certain city block is in the form of a parallelogram. Two of its sides are each 421 ft. long; the other two sides are each 227 ft. in length. If the distance between the first pair of sides is 126 ft., find the area of the land in the block, and the length of the diagonals.
To find the area of the land in the block, you can use the formula for the area of a parallelogram: A = base × height. In this case, the base is the distance between the first pair of sides, and the height is the length of one of the other sides.
Given:
Base (b) = 126 ft
Height (h) = 421 ft
Now, we can calculate the area using the formula:
A = b × h
A = 126 ft × 421 ft
A = 53046 ft²
Therefore, the area of the land in the block is 53046 square feet.
To find the length of the diagonals of the parallelogram, we can apply the Pythagorean theorem. The diagonal of a parallelogram bisects it into two congruent triangles.
Given:
Side 1 (a) = 421 ft
Side 2 (b) = 227 ft
To find the length of the diagonal (c), we can use the Pythagorean theorem formula:
c² = a² + b²
c² = 421 ft² + 227 ft²
c² = 178041 ft² + 51529 ft²
c² = 229570 ft²
Taking the square root of both sides to solve for c:
c = √(229570 ft²)
c ≈ 479.29 ft
Therefore, the length of the diagonals of the parallelogram is approximately 479.29 feet.
as with all parallelograms,
A = Bh