Question

A rectangular pyramid has a height of 8 meters. The base is 7 meters in length and 15 meters in width two different triangular cross sections are formed through the vertex and perpendicular to the base and to each other. What is the difference in the areas of the cross section? help- please-

Answer 1

Answer:

The difference in the areas of the cross section is 32 m²

Step-by-step explanation:

The given parameters are;

The height of the rectangular pyramid = 8 meters

The length of the base of the pyramid = 7 meters

The width of the base of the pyramid = 15 meters

Whereby triangular cross sections are formed through the vertex and perpendicular to the base, and to each other, we have;

The sides of the two triangles consists of the following;

1) Two slant height of the pyramid each

2) The two perpendicular lines joining the midpoints of the opposite sides of the base of the pyramid with length equal to the length of the adjacent side to the sides from which they are drawn which are 15 meters and 7 meters

3) The two lines and the corresponding slant height form triangles cross section which are perpendicular to each other.

the slant height, $h_l$, is given as follows;

$h_l$ = √(8² + (15/2)²) ≈ 10.966

For the triangular cross section with base = 15 m

The area of the cross section = 1/2 × Base₁₅ × Height = 1/2 × 15 m × 8 m = 60 m²

For the triangular cross section with base = 7 m

The area of the cross section = 1/2 × Base₇ × Height = 1/2 × 7 m × 8 m = 28 m²

The difference in the areas of the cross section = 60 m² - 28 m² = 32 m².