This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here are the area and perimeter for each shape: a) Right-angled triangle Step 1: Calculate the length of the hypotenuse using the Pythagorean theorem. c = sqrt(9^2 + 12^2) = sqrt(81 + 144) = sqrt(225) = 15 cm Step 2: Calculate the area of the triangle. A = (1)/(2) × base × height = (1)/(2) × 12 cm × 9 cm = 54 cm^2 Step 3: Calculate the perimeter of the triangle. P = side_1 + side_2 + side_3 = 9 cm + 12 cm + 15 cm = 36 cm The area is 54 cm^2 and the perimeter is 36 cm. b) Rectangle Step 1: Calculate the area of the rectangle. A = length × width = 15 cm × 5 cm = 75 cm^2 Step 2: Calculate the perimeter of the rectangle. P = 2 × (length + width) = 2 × (15 cm + 5 cm) = 2 × 20 cm = 40 cm The area is 75 cm^2 and the perimeter is 40 cm. c) Circle Step 1: Calculate the area of the circle. A = r^2 = (8 mm)^2 = 64 mm^2 ≈ 201.06 mm^2 Step 2: Calculate the perimeter (circumference) of the circle. C = 2 r = 2 (8 mm) = 16 mm ≈ 50.27 mm The area is 64 mm^2 ≈ 201.06 mm^2 and the perimeter is 16 mm ≈ 50.27 mm. d) Rhombus Step 1: Calculate the area of the rhombus. A = (1)/(2) × d_1 × d_2 = (1)/(2) × 24 mm × 52 mm = 12 mm × 52 mm = 624 mm^2 Step 2: Calculate the perimeter of the rhombus. P = 4 × side = 4 × 21 mm = 84 mm The area is 624 mm^2 and the perimeter is 84 mm. Send me the next one 📸