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
Here are the areas of the shapes: a) Step 1: Decompose the shape into a rectangle and a triangle. The rectangle has a width of 4 mm and a height of 3 mm. The triangle has a base of 11 mm - 4 mm = 7 mm and a height of 3 mm. Step 2: Calculate the area of the rectangle. A_rectangle = width × height = 4 mm × 3 mm = 12 mm^2 Step 3: Calculate the area of the triangle. A_triangle = (1)/(2) × base × height = (1)/(2) × 7 mm × 3 mm = (21)/(2) mm^2 = 10.5 mm^2 Step 4: Calculate the total area of shape (a). A_(a) = A_rectangle + A_triangle = 12 mm^2 + 10.5 mm^2 = 22.5 mm^2 b) Step 1: Decompose the shape into a large trapezoid and a small rectangular cut-out. The large trapezoid has parallel sides of 7 m and 17 m, and a height of 5 m. The cut-out rectangle has a width of 2 m and a height of 3 m. Step 2: Calculate the area of the large trapezoid. A_trapezoid = (1)/(2) × (sum of parallel sides) × height A_trapezoid = (1)/(2) × (7 m + 17 m) × 5 m A_trapezoid = (1)/(2) × 24 m × 5 m = 12 m × 5 m = 60 m^2 Step 3: Calculate the area of the cut-out rectangle. A_cut-out = width × height = 2 m × 3 m = 6 m^2 Step 4: Calculate the total area of shape (b). A_(b) = A_trapezoid - A_cut-out A_(b) = 60 m^2 - 6 m^2 = 54 m^2 Send me the next one 📸