1. The diameter of a basketball rim is 18 inches. A standard basketball has a circumference of 30 inches. What is the distance between the ball and the rim in a shot in which the ball goes exactly in the center of the rim? Show your work.
2. A park in a subdivision has a triangular shape. Two adjacent sides of the park are 533 feet and 525 feet. The angle between the sides is 53°. Find the area of the park to the nearest square foot.
3. Find the area of a regular hexagon with an apothem 10.4 yards long and a side 12 yards long. Round your answer to the nearest tenth.
4. What is the area of the kite?
A kite with both diagonals is shown. The diagonals intersect each other so that the shorter diagonal is split into parts that are 2 feet and 2 feet and the longer diagonal is split into parts that are 10 feet and 20 feet.
5. find the area. The figure is not drawn to scale.
A triangle with side 6.9 cm extends to form a second right triangle with a height of 4cm.
6. A picture of a parallelogram with width 38in. and side 44in. A perpendicular line with a height of 35in. is shown inside the parallelogram and forms a right triangle.
Find the area of the parallelogram. The figure is not drawn to scale.
(3 points)
1. The distance between the ball and the rim in a shot where the ball goes exactly in the center of the rim is equal to half the circumference of the basketball minus the radius of the rim:
Distance = (30 inches / 2) - (18 inches / 2)
Distance = 15 inches - 9 inches
Distance = 6 inches
2. To find the area of the triangular park, we can use the formula:
Area = (1/2) * side1 * side2 * sin(angle)
Area = (1/2) * 533 ft * 525 ft * sin(53°)
Area ≈ 140,793 ft²
3. The formula for the area of a regular hexagon is A = (3√3 * side²) / 2 * apothem
Area = (3√3 * 12²) / 2 * 10.4
Area ≈ 249.3 square yards
4. To find the area of the kite, we can use the formula:
Area = (1/2) * diagonal1 * diagonal2
Area = (1/2) * (2 ft + 2 ft) * (10 ft + 20 ft)
Area = (1/2) * 4 ft * 30 ft
Area = 60 square feet
5. The area of the two combined triangles can be found by adding the areas of each triangle separately:
Area1 = (1/2) * base * height
Area1 = (1/2) * 6.9 cm * 4 cm
Area1 = 13.8 cm²
Area2 = (1/2) * base * height
Area2 = (1/2) * 6.9 cm * 35 cm
Area2 = 120.75 cm²
Total Area = Area1 + Area2
Total Area = 13.8 cm² + 120.75 cm²
Total Area = 134.55 cm²
6. To find the area of the parallelogram, we can use the formula:
Area = base * height
Area = 38 in * 35 in
Area = 1330 square inches