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
a) Step 1: Identify the dimensions of the rectangular part. The width of the rectangle is 10 m and the height is 6 m. Step 2: Calculate the area of the rectangular part. Area_rectangle = width × height Area_rectangle = 10 m × 6 m Area_rectangle = 60 m^2 The area of the rectangular part is 60 m^2. b) Step 1: Identify the dimensions of the triangular part. The base of the triangle is 10 m and the perpendicular height is 4 m. Step 2: Calculate the area of the triangular part. Area_triangle = (1)/(2) × base × perpendicular height Area_triangle = (1)/(2) × 10 m × 4 m Area_triangle = 5 m × 4 m Area_triangle = 20 m^2 The area of the triangular part is 20 m^2. c) Step 1: Add the areas of the rectangular and triangular parts. Total Area = Area_rectangle + Area_triangle Total Area = 60 m^2 + 20 m^2 Total Area = 80 m^2 The total area of the composite shape is 80 m^2. d) Step 1: Identify all the external sides that form the perimeter. The perimeter consists of the base of the rectangle (10 m), the two vertical sides of the rectangle (6 m each), and the two slant sides of the triangle (6.40 m each). Step 2: Calculate the total perimeter. Perimeter = rectangle base + 2 × rectangle height + 2 × triangle slant side Perimeter = 10 m + (2 × 6 m) + (2 × 6.40 m) Perimeter = 10 m + 12 m + 12.80 m Perimeter = 34.80 m The perimeter of the shape is 34.80 m. That's 2 down. 3 left today — send the next one.