Question

This rectangular prism is intersected by a plane that contains points B, D, H, and F.

Answer 1

Answer:

The perimeter of the cross section is 33.3 cm

Step-by-step explanation:

Given: A rectangular prism with height 6 centimeters, length 8 centimeters, and width 7 centimeters. The rectangular prism is intersected by a plane that contains points B, D, H, and F.

We have to determine the perimeter of the cross section.

Since, The plane is drawn diagonally such that it intersect the points  B, D, H, and F.(as shown in figure below)

Perimeter of a figure is the sum of its outer boundaries.

We first find the length of diagonal HF.

Since, HGFE , is a rectangle

So, Diagonal of rectangle is given by

$D=\sqrt{Length^2+breadth^2}$

Here, Length = 8 cm

and breadth = 7 cm

So, $D=\sqrt{8^2+7^2}=\sqrt{64+49}\approx 10.63$

Thus, HF = DB = 10.63 cm

Therefore, Perimeter of cross section is DB + BF +FH + DH

= 10.63 + 6 + 6 + 10.63 = 33.26

Thus, the perimeter of the cross section is 33.3 cm