Question

A triangular shaped glass with vertices at A (-5,-4), B(1,6) and C(7,-4) has to be painted. If one buckket of paint covers 6 square feet, how many bucke ts of paint will berequired to paint the whole glass, if only one coat of paint is applied.​

Answer 1

Given :

• A triangular shaped glass with vertices at A (-5,-4), B(1,6) and C(7,-4)
• Area of the paint cans = 6

To Find :

• Number of paint cans required

Solution :

Points = A (-5,-4) , B(1,6) and C(7,-4)

A (-5,-4)

• x₁ = -5
• y₁ = -4

B (1,6)

• x₃ = 1
• y₃ = 6

C(7,-4)

• x₂ = 7
• y₂ = -4

$\\ \\ \\ \tt \longrightarrow \: Area \: of \: \Delta ABC \: = \: \dfrac{1}{2} \binom{ x1 \: \: \: \: x2 \: \: \: \: x3 \: \: \: \: x1}{y1 \: \: \: \: y2 \: \: \: \: y3 \: \: \: \: y1}sq.units \\ \\ \\ \tt \longrightarrow \: Area \: of \: \Delta ABC \: = \: \dfrac{1}{2} \binom{ - 5 \: \: \: \: 7 \: \: \: \: 1 \: \: - 5}{ - 4 \: \: - 4 \: \: \: \: 6 \: \: - 4} \\ \\ \\ \tt \longrightarrow \:Now \: we \: have \: to \: cross \: multiply....\\ \\ \\ \tt \longrightarrow \: Area \: of \: \Delta ABC \: = \: \dfrac{1}{2} \: [ \: (20 + 42 - 4) - ( - 28 - 4 - 30) \: ] \\ \\ \\ \tt \longrightarrow \: Area \: of \: \Delta ABC \: = \: \dfrac{1}{2} \:[ \: (62 - 4) - ( - 62) \: ] \\ \\ \\ \tt \longrightarrow \: Area \: of \: \Delta ABC \: = \: \dfrac{1}{2} \times (58 + 62) \\ \\ \\ \tt \longrightarrow \: Area \: of \: \Delta ABC \: = \: \dfrac{1}{2} \times 120 \\ \\ \\ \tt \longrightarrow \: Area \: of \: \Delta ABC \: = \:60sq.units$

•°• No of paint cans required = 10

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★ VERIFICATION :

$\\ \\ \\ \tt \longrightarrow \: \frac{ Area \: of \: the \: \Delta ABC }{Area \: of \: the \:paint \: cans} \\ \\ \\ \tt \longrightarrow \: \frac{60}{6} \\ \\ \\ \tt \longrightarrow \:10cans$