Question

Select the correct answer.A company makes the forks for forklift trucks. Each fork has the dimensions shown. The top of each fork is painted. To the nearest squaremillimeter, how much area is painted on the top of each fork?OA. 83,425 mm²OB. 81,000 mm²OC. 84,118 mm²OD. 2,425 mm²

Answer 1

The correct option is A. 83425 square in

Step-by-step explanation:

We can divide the fork in to a rectangle and a trapezoid.

The area of a rectangle is:

`A_(rectangle)=b\cdot h`

Where b is the base and h is the height.

The area of a trapezoid:

`A_(trapezoid)=(1)/(2)h(b_1+b_2)`

Where h is the height, b1 and b2 are the bases.

We don't know the height of the trapezoid, but we can find it.

If we draw:

We can find the height using the trigonometric ratio sine, where:

h is the opposite leg

the hypotenuse is 40 mm

the angle is 60º

`\sin(60º)=(h)/(40)`
`\begin{gathered} 40\cdot\sin(60º)=h \\ h=40\cdot(√(3))/(2)=20√(3)mm \end{gathered}`

Now, we can find the area of the trapezoid using:

h = 20√3 mm

b1 = 90 mm

b2 = 50 mm

`A_(trapezoid)=(1)/(2)\cdot20√(3)\cdot(90+50)=10√(3)\cdot140=1400√(3)\approx2424.871mm^2`

And the area of the rectangle using:

b = 900 mm

h = 90 mm

`A_(rectangle)=900\cdot90=81000mm^2`

If we add the two areas, we get the total area:

`81000+2424.871=83424.871mm^2`

Thus, the area to the nearest square millimeter is 83,424mm², which is option A