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
Step 1: Calculate the length of side AB. The diagonals of a kite are perpendicular. Therefore, AEB is a right-angled triangle. Using the Pythagorean theorem: AB^2 = AE^2 + BE^2 AB^2 = 3^2 + 4^2 AB^2 = 9 + 16 AB^2 = 25 AB = sqrt(25) AB = 5 cm Step 2: Calculate the length of side DA. Similarly, DEA is a right-angled triangle. DA^2 = DE^2 + AE^2 DA^2 = 4^2 + 3^2 DA^2 = 16 + 9 DA^2 = 25 DA = sqrt(25) DA = 5 cm Step 3: Calculate the length of side BC. BEC is a right-angled triangle. BC^2 = BE^2 + CE^2 BC^2 = 4^2 + 6^2 BC^2 = 16 + 36 BC^2 = 52 BC = sqrt(52) BC = sqrt(4 × 13) BC = 2sqrt(13) cm Step 4: Calculate the length of side CD. CED is a right-angled triangle. CD^2 = CE^2 + DE^2 CD^2 = 6^2 + 4^2 CD^2 = 36 + 16 CD^2 = 52 CD = sqrt(52) CD = sqrt(4 × 13) CD = 2sqrt(13) cm Step 5: Calculate the perimeter of the kite. The perimeter is the sum of all side lengths: P = AB + BC + CD + DA P = 5 + 2sqrt(13) + 2sqrt(13) + 5 P = 10 + 4sqrt(13) cm Using sqrt(13) ≈ 3.6055: P ≈ 10 + 4(3.6055) P ≈ 10 + 14.422 P ≈ 24.42 cm The perimeter of the kite is 10 + 4sqrt(13) cm or approximately 24.42 cm. Step 6: Calculate the area of the kite. The area of a kite is given by the formula A = (1)/(2) d_1 d_2, where d_1 and d_2 are the lengths of the diagonals. Length of diagonal AC = AE + CE = 3 + 6 = 9 cm. Length of diagonal BD = BE + DE = 4 + 4 = 8 cm. A = (1)/(2) × AC × BD A = (1)/(2) × 9 × 8 A = (1)/(2) × 72 A = 36 cm^2 The area of the kite is 36 cm^2. Send me the next one 📸