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.
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Here are the solutions to the problems. Problem 1: a) Find the area of Mr. Bintum's house. Step 1: Calculate the area of section A (semicircle). The diameter of the semicircle is 14m, so the radius r = 14m2 = 7m. The area of a semicircle is given by A_A = (1)/(2) r^2. We will use ≈ 3.14. A_A = (1)/(2) × 3.14 × (7m)^2 A_A = (1)/(2) × 3.14 × 49m^2 A_A = 1.57 × 49m^2 A_A = 76.93 m^2 Step 2: Calculate the area of section B (rectangle). The length of the rectangle is 20m and the width is 14m. The area of a rectangle is given by A_B = length × width. A_B = 20m × 14m A_B = 280 m^2 Step 3: Calculate the area of section C (triangle). The height of the triangle is 3m and the hypotenuse is 5m. First, find the base using the Pythagorean theorem (a^2 + b^2 = c^2). Let the base be b. b^2 + (3m)^2 = (5m)^2 b^2 + 9m^2 = 25m^2 b^2 = 25m^2 - 9m^2 b^2 = 16m^2 b = sqrt(16m)^2 b = 4m The area of a triangle is given by A_C = (1)/(2) × base × height. A_C = (1)/(2) × 4m × 3m A_C = 6 m^2 Step 4: Calculate the total area of Mr. Bintum's house. Total Area = A_A + A_B + A_C Total Area = 76.93 m^2 + 280 m^2 + 6 m^2 Total Area = 362.93 m^2 The area of Mr. Bintum's house is 362.93 m^2. b) Find how much Mr. Bintum will spend if he decides to put tiles on the floor of the kitchen at the cost of 2500 FRS per m^2. Step 1: Identify the area of the kitchen. The kitchen is section C, which has an area of 6 m^2. Step 2: Calculate the total cost of tiling. Cost = Area of kitchen × Cost per m^2 Cost = 6 m^2 × 2500 FRS/m^2 Cost = 15,000 FRS Mr. Bintum will spend 15,000 FRS to tile the kitchen. Problem 4: Find the cost of painting the walls at 200 FRS per square meter. Step 1: Calculate the total area of the walls. The party hall measures 20m long, 18m wide, and 8m high. Area of two walls (length × height) = 2 × (20m × 8m) 2 × 160 m^2 = 320 m^2 Area of two walls (width × height) = 2 × (18m × 8m) 2 × 144 m^2 = 288 m^2 Total wall area = 320 m^2 + 288 m^2 = 608 m^2. Step 2: Calculate the area of the doors and windows. There are two large doors, each measuring 3m by 2m. Area of two doors = 2 × (3m × 2m) 2 × 6 m^2 = 12 m^2 There are four large windows, each measuring 4m by 4m. Area of four windows = 4 × (4m × 4m) 4 × 16 m^2 = 64 m^2 Total area of doors and windows = 12 m^2 + 64 m^2 = 76 m^2. Step 3: Calculate the area to be painted. Area to be painted = Total wall area - Area of doors and windows Area to be painted =