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Calculate the total area of Mr. Bintum's house, which is composed of a semicircle, a rectangle, and a triangle.

Mathematics

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a) Find the area of Mr. Bintum's house.

Step 1: Calculate the area of section A (semicircle).
The diameter of the semicircle is 14m14\text{m}, so the radius r=14m2=7mr = \frac{14\text{m}}{2} = 7\text{m}.
The area of a semicircle is given by AA=12πr2A_A = \frac{1}{2}\pi r^2. We will use π≈3.14\pi \approx 3.14.

AA=12×3.14×(7m)2A_A = \frac{1}{2} \times 3.14 \times (7\text{m})^2 AA=12×3.14×49m2A_A = \frac{1}{2} \times 3.14 \times 49\text{m}^2 AA=1.57×49m2A_A = 1.57 \times 49\text{m}^2 AA=76.93 m2A_A = 76.93\text{ m}^2

Step 2: Calculate the area of section B (rectangle).
The length of the rectangle is 20m20\text{m} and the width is 14m14\text{m}.
The area of a rectangle is given by AB=length×widthA_B = \text{length} \times \text{width}.

AB=20m×14mA_B = 20\text{m} \times 14\text{m} AB=280 m2A_B = 280\text{ m}^2

Step 3: Calculate the area of section C (triangle).
The height of the triangle is 3m3\text{m} and the hypotenuse is 5m5\text{m}. First, find the base using the Pythagorean theorem (a2+b2=c2a^2 + b^2 = c^2).
Let the base be bb.

b2+(3m)2=(5m)2b^2 + (3\text{m})^2 = (5\text{m})^2 b2+9m2=25m2b^2 + 9\text{m}^2 = 25\text{m}^2 b2=25m2−9m2b^2 = 25\text{m}^2 - 9\text{m}^2 b2=16m2b^2 = 16\text{m}^2 b=16m2b = \sqrt{16\text{m}^2} b=4mb = 4\text{m}

The area of a triangle is given by AC=12×base×heightA_C = \frac{1}{2} \times \text{base} \times \text{height}.

AC=12×4m×3mA_C = \frac{1}{2} \times 4\text{m} \times 3\text{m} AC=6 m2A_C = 6\text{ m}^2

Step 4: Calculate the total area of Mr. Bintum's house.
Total Area = AA+AB+ACA_A + A_B + A_C

Total Area=76.93 m2+280 m2+6 m2\text{Total Area} = 76.93\text{ m}^2 + 280\text{ m}^2 + 6\text{ m}^2 Total Area=362.93 m2\text{Total Area} = 362.93\text{ m}^2

The area of Mr. Bintum's house is 362.93 m2\boxed{\text{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 m2^2.

Step 1: Identify the area of the kitchen.
The kitchen is section C, which has an area of 6 m26\text{ m}^2.

Step 2: Calculate the total cost of tiling.
Cost = Area of kitchen ×\times Cost per m2^2

Cost=6 m2×2500 FRS/m2\text{Cost} = 6\text{ m}^2 \times 2500 \text{ FRS/m}^2 Cost=15,000 FRS\text{Cost} = 15,000 \text{ FRS}

Mr. Bintum will spend 15,000 FRS\boxed{\text{15,000 FRS}} to tile the kitchen.

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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 20m20\text{m} long, 18m18\text{m} wide, and 8m8\text{m} high.
Area of two walls (length ×\times height) = 2×(20m×8m)2 \times (20\text{m} \times 8\text{m})

2×160 m2=320 m22 \times 160\text{ m}^2 = 320\text{ m}^2

Area of two walls (width ×\times height) = 2×(18m×8m)2 \times (18\text{m} \times 8\text{m})

2×144 m2=288 m22 \times 144\text{ m}^2 = 288\text{ m}^2

Total wall area = 320 m2+288 m2=608 m2320\text{ m}^2 + 288\text{ m}^2 = 608\text{ m}^2.

Step 2: Calculate the area of the doors and windows.
There are two large doors, each measuring 3m3\text{m} by 2m2\text{m}.
Area of two doors = 2×(3m×2m)2 \times (3\text{m} \times 2\text{m})

2×6 m2=12 m22 \times 6\text{ m}^2 = 12\text{ m}^2

There are four large windows, each measuring 4m4\text{m} by 4m4\text{m}.
Area of four windows = 4×(4m×4m)4 \times (4\text{m} \times 4\text{m})

4×16 m2=64 m24 \times 16\text{ m}^2 = 64\text{ m}^2

Total area of doors and windows = 12 m2+64 m2=76 m212\text{ m}^2 + 64\text{ m}^2 = 76\text{ m}^2.

Step 3: Calculate the area to be painted.
Area to be painted = Total wall area - Area of doors and windows

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