The shape of the area of the lawn that is to be treated with weedkiller is a
trapezoid.
The total cost of the cans of weedkiller needed to cover the lawn is £59.25
Reasons:
The given information are;
A rea covered by one can of weedkiller = 100 m²
The cost of each can = £19.75
The shape of the lawn = A trapezium
Required:
The cost of the cans of weedkiller needed to cover the lawn
Solution:
[tex]The \ area \ of \ the \ trapezoid = \dfrac{a + b}{2} \times h[/tex]
Where;
a = Top horizontal base = 12 m
b = Lower horizontal base = 20 m
h = The height = Length of the fence
Taking, the fence as being perpendicular to the 12 m, and 20 m sides, we have;
Translating the slant 17 m side, 12 m to the left, gives a right triangle, of
base length, l = 20 m - 12 m = 8 m
Therefore, by Pythagoras theorem;
Length of the fence, h = √(17² - 8²) = 15
h = 15 m
Which gives;
[tex]Area \ of \ the \ trapezoidal \ lawn = \dfrac{12 + 20}{2} \times 15 = 240[/tex]
The area of the trapezoidal lawn, A = 240 m²
Area per can, Cₐ = 100 m²/can
Therefore;
[tex]Number \ of \ cans \ required = \dfrac{A}{C_a} = \dfrac{240}{100} = 2.4[/tex]
The unit of weedkiller sold = 1 can per unit
Therefore;
Number of cans needed to be bought cover the lawn = 2 cans + 1 extra can, for the 0.4 more weedkiller needed
Which gives;
The number of cans of weedkiller to be bought = 3 cans of weedkiller
Total cost of the 3 cans of weedkiller = 3 × £19.75 = £59.25
The total cost of the cans of weedkiller needed to cover the lawn = £59.25
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