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: Identify the base and calculate the perpendicular height of the outer triangle. From the previous image (the net), the outer triangles ("The Back" and "The Front") are isosceles triangles. The base of the triangle is 150 mm. The two equal slanted sides are 215 mm each. To find the perpendicular height (h), we can use the Pythagorean theorem. The height divides the isosceles triangle into two right-angled triangles, where half of the base is one leg, the height is the other leg, and the slanted side is the hypotenuse. Half of the base = 150 mm2 = 75 mm. Using the Pythagorean theorem (a^2 + b^2 = c^2): h^2 + (75 mm)^2 = (215 mm)^2 h^2 + 5625 mm^2 = 46225 mm^2 h^2 = 46225 mm^2 - 5625 mm^2 h^2 = 40600 mm^2 h = sqrt(40600) mm h ≈ 201.4944 mm Step 2: Calculate the area of the outer triangle using the given formula. The formula for the area of a triangle is: Area = (1)/(2) × Base × Perpendicular height Substitute the values for the base and the calculated perpendicular height: Area = (1)/(2) × 150 mm × sqrt(40600) mm Area = 75 mm × sqrt(40600) mm Area ≈ 75 × 201.4944 mm^2 Area ≈ 15112.08 mm^2 The area of the outer triangle is approximately 15112.08 mm^2. That's 2 down. 3 left today — send the next one.