A triangular metal plate with a triangular metal plate placed in a box with a regular triangular prism with all the side edges 3 dm. It rests on the edge of the base and is inclined to the bottom of the box at an angle of 60 °. Calculate the area of the plate 0.01 dm2 accuracy. Take a look at how the spacing between planes is measured.

6.75 dm²

Step-by-step explanation:

All the side edges in the regular triangular prism are 3 dm long. Then, the base of the triangular plate is 3 dm long, and the other two sides are: √[3² + 3²] = 4.24 dm long (a right triangle is made and Pythagorean theorem is applied).

The height of the triangular plate is: √[4.24² + 1.5²] = 4.5 dm long (again Pythagorean theorem is applied)

Area of the triangular plate is: base*height/2 = 3*4.5/2 = 6.75 dm²

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