Assessing Maths Assignment sample essay

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I’ve been asked me to cost his landscaping project for him using the prices quoted by a local supplier, and to give him a full breakdown of the calculations required and how I arrived at the final cost. Plan I plan to do this firstly by breaking up the garden plan into 5 sections. 1. Decking and border. 2. Flowerbed and crazy paving 3. Fish pond, safety fence, bridge and rail 4. Perimeter fence 5. Grass. Decking and Border The decking area consists of two right angle triangle. The two edges around the decking are equal in length. I need to work out the length of the edges and the area of the decking, how much materials required and cost.

In the 1st triangle marked A, I need to work out the length the opposite side of the triangle with the angle 69?. I will do this by using trigonometry tan equation. Tan ? = Tan 69 = If I subtract 4m from the above, this will give me the length of ? the border as each side of the border is equal. I will then work out the base of the 2nd triangle marked B using Pythagoras theorem (the square of the hyp) = (the sum of the other 2 sides). hyp? = x? + 4? I will then work out the area of the two triangles with the equation A = ? x base x perpendicular height A = ? ? b ? h

By adding the two areas of the triangle together I will get the total area of the two triangles. Using the total area of the decking I will then work out how many m? required, and then calculate the price at ? 25. 00 + VAT per m?. Using the length of the border I will work out how many strips required at 2m strips and calculate the price at ? 10. 00 per 2m strips. Finally by adding the cost of the border and the decking will get the total cost of the decking area. Flowerbed and Crazy Paving The flowerbed is a semi-circle positioned along an 8m side, surrounded by a 0.

5m wide crazy paving and filled with bulbs. 1st I will decide what size of semi-circle the flowerbed will be and work out the radius I need to work out the area of the semi-circle marked C. the flowerbed using the equation, this will give me the service area of the flower bed Area + I then will work out the area of the larger semi-circle marked D using the above equation and subtract the area of the smaller circle (flowerbed). This will give me the area of the crazy paving I will then work out how much crazy paving required / m?. I will then work out the cost of the paving @ ? 3. 50 + VAT per m?

I will work out how many bulbs required for the area in m? for the flower bed, and the cost at ? 6. 40 per m?. Fish pond, safety fence, bridge and rail The fish pond has a depth of 75cm enclosed by a safety fence which has a 1m wide bridge over it in the shape of a quadrant. The bridge is fitted with a handrail on both sides. Firstly I need to decide what length the sides of the pond are going to be. (Pond marked E) To work out the amount of safety fence required, I will work out the perimeter of the square fish pond subtracting 2m (1m for each side of the bridge at 1m each side).

Perimeter = 4 x sides – 2(1m) I will need to work out how many meters of safety fencing/ m required and then cost it at ? 8. 70 per m To work out the quadrant shape bridge marked F. As a quadrant is quarter of a circle I can work out the length of the outside edge of the bridge by using the circle theorem. I will calculate the circumference using the radius and dividing by 4. Equation to find Quadrant Circumference = When will then cost the bridge with the local supplier’s prices. ?35. 00 (