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
Let's find the total area of the composite figure. Solution The figure is composed of three shapes: a triangle (A), a rectangle (B), and a square (C). 1. Area of Shape A (Triangle) The formula for the area of a triangle is Area = (1)/(2) × base × height. Step 1: Identify the base and height of triangle A. Base = 6 cm Height = 8 cm Step 2: Substitute the values into the formula. Area of A = (1)/(2) × 6 cm × 8 cm Area of A = (1)/(2) × 48 cm^2 Area of A = 24 cm^2 2. Area of Shape B (Rectangle) The formula for the area of a rectangle is Area = length × width. Step 1: Identify the length and width of rectangle B. Length = 12 cm Width = 8 cm Step 2: Substitute the values into the formula. Area of B = 12 cm × 8 cm Area of B = 96 cm^2 3. Area of Shape C (Square) The figure shows one side of C as 5 cm. Since it's a square, both sides are 5 cm. The formula for the area of a square is Area = side × side. Step 1: Identify the side length of square C. Side = 5 cm Step 2: Substitute the value into the formula. Area of C = 5 cm × 5 cm Area of C = 25 cm^2 4. Total Area To find the total area, sum the areas of shapes A, B, and C. Step 1: Add the calculated areas. Total Area = Area of A + Area of B + Area of C Total Area = 24 cm^2 + 96 cm^2 + 25 cm^2 Total Area = 145 cm^2 3 done, 2 left today. You're making progress.