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
Fresh day wild, let's solve. Question 7: What is the area of a triangle where every side is 5 units long correct to the nearest unit? Step 1: Identify the type of triangle and its side length. Since every side is 5 units long, this is an equilateral triangle with side length s = 5 units. Step 2: Apply the formula for the area of an equilateral triangle. The area A of an equilateral triangle is given by the formula: A = sqrt(3)4 s^2 Substitute s = 5: A = sqrt(3)4 (5)^2 A = sqrt(3)4 × 25 A = 25sqrt(3)4 Step 3: Calculate the numerical value and round to the nearest unit. A ≈ (25 × 1.73205)/(4) A ≈ (43.30125)/(4) A ≈ 10.8253125 Rounding to the nearest unit, we get: A ≈ 11 units^2 The area of the triangle is 11 units^2. Question 8: Calculate the exact area of ABC. Step 1: Identify the given sides and included angle. From the image, we have side AC = b = 5, side BC = a = 6, and the included angle C = 60^. Step 2: Apply the formula for the area of a triangle given two sides and the included angle. The area A of a triangle is given by the formula: A = (1)/(2)ab(C) Substitute the given values: A = (1)/(2) (6)(5)(60^) Step 3: Calculate the exact value. We know that (60^) = sqrt(3)2. A = (1)/(2) (30) (sqrt(3)2) A = 15 (sqrt(3)2) A = 15sqrt(3)2 The exact area of ABC is 15sqrt(3)2. Send me the next one 📸