The height of the correct prism ABCDA1B1C1D1 is 16 cm. The side of its base is 15 cm. Calculate the perimeter

| August 12, 2021 | education

The height of the correct prism ABCDA1B1C1D1 is 16 cm. The side of its base is 15 cm. Calculate the perimeter of the prism section by the plane containing the straight line A1B1 and the midpoint of the edge DD1.

Since the prism is correct, at its base lies a square with a side of 15 cm.

The section containing the straight line A1B1 and the middle of the edge DD1 is a rectangle A1B1HP, which has two sides with the sides of the base of the prism, and the other two are hypotenuses of right-angled triangles.

Let’s draw the line of the RK parallel to the AD. Since point P is the middle of DD1, then point K is the middle of AA1.

Then KA1 = AA1 / 2 = 16/2 = 8 cm.

From the right-angled triangle А1РК we define the hypotenuse А1Р.

A1P ^ 2 = KA1 ^ 2 + KP ^ 2 = 64 + 225 = 289.

A1P = 17 cm.

Determine the perimeter of the section.

Pa1v1nr = 2 * (A1P + A1B1) = 2 * (17 + 15) = 64 cm.

Answer: The perimeter of the section is 64 cm.



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