Check the solutions to the rhombus problems:
1. Find the area and perimeter of a rhombus: Given: Side length (a) = 8 inches
- Area (A): A = a * h = 8 inches * h (since the height is not given)
- Perimeter (P): P = 4 * a = 4 * 8 inches
2. Calculate the diagonal lengths: Given: Area (A) = 48 square inches, Length of one diagonal (q) = 10 inches
- Length of the other diagonal (d2): d2 = (2 * A) / q = (2 * 48 square inches) / 10 inches
3. Determine the inradius: Given: Area (A) = 36 square inches, Side length (a) = 6 inches
- Inradius (r): r = A / (2 * a) = 36 square inches / (2 * 6 inches)
4. Find the circumradius: Given: Length of the horizontal diagonal (p) = 12 inches, Length of the vertical diagonal (q) = 9 inches
- Circumradius (R): R = 0.5 * √(p² + q²) = 0.5 * √((12 inches)² + (9 inches)²)
5. Calculate the area of a rhombus: Given: Length of two adjacent sides (e and f) = 7 inches, Included angle (angle) = 60 degrees
- Area (A): A = (e * f) / 2 = (7 inches * 7 inches) / 2 * sin(60 degrees)
6. Find the side length of a rhombus: Given: Length of the horizontal diagonal (p) = 10 inches, Length of the vertical diagonal (q) = 6 inches
- Length of one side (a): a = √((p/2)² + (q/2)²) = √((10 inches/2)² + (6 inches/2)²)
7. Calculate the area of a rhombus: Given: Length of one side (a) = 5 feet, Height (h) = 8 feet
- Area (A): A = a * h = 5 feet * 8 feet
Please note that for problems 1 and 5, additional information may be needed (height or angle in degrees) to calculate the area accurately.