A lake has the following lenghts, in order: 100m, 150m, 200m, 175m, 250m, 150m, 100m, 50m. The lengths were measured at intervals of 50m, what is the surface area of the lake?
A cieling need to be covered. Measurements are taken every 10 inches, and the lengths are recorded as 100in, 150in, 200in, 150in, 200in, 200in, 150in, 200in and 50in. What is the area of the ceiling?
A floor needs to be covered in vinyl carpet. The floor however is irregularly shaped and measures, from one end to the other, in order, 10m, 30m, 50m, 60m, 20m, 20m, 30m, 10m and 5m. How large is the floor if teh measurements are taken every 2m?
A cover is built for a reservoir located in a natural landform. Surveyors measure the landform's width every 10 metres and record the following distances: 125m, 130m, 190m, 230m, 200m, 180m, 150m.
The first and last distnaces across a plot of land are 60 feet and 100 feet respectively. The other distances are 80ft, 100ft, 120ft, 100ft, 90ft and 110ft. How big is the plot of land?
What is the area of a figure that measures 1, 2, 4, 5, 3, 2, 1 and 8 inches across, respectively, if the measurements are taken every 0.5 inches?
A satellite photograph covers an island. The key on the island shows that the distances across the island are, from left to right, 100km, 120km, 300km, 200km, 180km, 100km, 150km and 175km. If the measurements are 50km apart, how much surface area is there on the island?
A hole was broken on the side of a metal fence and it needs to be covered over with sheeting. If the hole measures, from top to bottom, at intervals of 15 cm, 1m, 50cm, 1.5m, 150cm, and 75cm, what area needs to be filled?
A painter paints an outline on the road, to be covered in white paint for an advertising spot. The outline is measured every 10 cm and is 50, 40, 30, 50, 45, 40 and 80cm wide, and 10 and 30 cm wide at the ends. How much area needs to be painted?
One end of a field is 100m wide, and the other end is 110m wide. How much area is there on the field for sports if every 15m the field is measured and the distances (excluding the other two already mentioned) are 105m, 110m, 108m, 103m, 97m, 98m, 105m and 103m?
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question 1
ReplyDeletelenght of strips = 100m, 150m, 200m, 175m, 250m, 150m, 100m, 50m.
Area = (width of strip)[(1/2)(sum of first and last oridnate) + (sum of other ordinates)].
width of strip = 50
using trapezoidial rule
area = (50)[(1/2)(150)+ (150m + 200m + 175m + 250m + 150m + 100m)
= (50)(1100)
= 55000m^2
question 2
ReplyDeletewidth of strips = 10in
length of strips = 100in, 150in, 200in, 150in, 200in, 200in, 150in, 200in and 50in.
Area = (width of strip)[(1/2)(sum of first and last oridnate) + (sum of other ordinates)].
area = (10)[(1/2)(100 + 50)(150in + 200in + 150in + 200in + 200in + 150in + 200in)]
area = 10 * 1325
= 13250in^2
question 3
ReplyDeletelength of strips in order = 10m, 30m, 50m, 60m, 20m, 20m, 30m, 10m and 5m.
width of strips = 2m
area = (width of strip)[(1/2)(sum of first and last oridnate) + (sum of other ordinates)].
area = (2)[(1/2)(10 + 5) + (30m + 50m + 60m + 20m + 20m + 30m + 10m)]
= (2)[227.5]
area of floor = 455m^2