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problem

Given that BC=BK=FI=5 units, CF=KI=3 units, CD=FG=IH=KJ=BE=6 units and that angle KBC = angle BCF = 90 °. MNOP is vertical plane parallel to surfaces BCFIK and EDGHJ and perpendicular to surface BCDE. MPQR is a horizontal plane parallel to surface BCDE.

Draw the orthogonal projection of the prism onto the horizontal plane PQRM.

I had a test at school and I was unable to solve this question. I failed at figuring out what should the horizontal distance from point K to point I would be. Show me how would you do it please.

And also help me choose a better tag for this if you can.

1 Answers 1

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When you project this prism straight down to the plane, you draw a vertical line from each vertex on the prism down to the plane. So, points F and C will both go down to the same spot. K and B will both be in the same place. The line BC will go straight down to the plane, and I will also go straight down and lay on that line.

To find out how far along the line BC the point 'I' will be, you can fill in the sides of the trapezoid drawn below over your figure. Since K and B are projected to the same point on the plane, finding the length of the straight, horizontal side of the trapezoid will show the distance between K and I in the plane.

enter image description here

With the projections into the plane drawn in, the side of the trapezoid that is highlighted in green moves straight down to the dotted line in the plane.

enter image description here

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    What do you mean when you said 'fill in the sides of the trapezoid drawn below over your figure" I understood everything you said except the part where you explain the process of finding the horizontal length of point K/B to point I. – 2017-01-04
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    I will add another diagram. – 2017-01-04
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    Thank you for trying to illustrate it for me. – 2017-01-04
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    I have to ask, it I were to calculate the length of I on the line BC/KF using the information they gave me. Would the right approach be drawing some lines against planes and subsequently employ the pythagorean theorem to them? – 2017-01-04