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Question
A triangular shaped glass with vertices at A(– 5, – 4), B(1, 6) and C(7, – 4) has to be painted. If one bucket of paint covers 6 square feet, how many buckets of paint will be required to paint the whole glass, if only one coat of paint is applied
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Solution
Given the vertices of the triangular glass is A (– 5, – 4), B (1, 6), and C (7, – 4)
Area of triangle ACB = `1/2[(x_1y_2 + x_2y_3 + x_3y_1) - (x_2y_1 + x_3y_2 + x_1y_3)]`
= `1/2[(20 + 42 - 4) - (-28 - 4 - 30)]`
= `1/2[58 - (- 62)]`
= `1/2 [58 + 62]`
= `1/2 xx 120`
= 60 sq. feet
Number of cans to paint 6 square feet = 1
∴ Number of cans = `60/6` = 10
⇒ Number of cans = 10
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