A rectangular pyramid has a height of 10 meters. The base measures 8 meters in length and 12 meters in width. Two different triangular cross sections are formed through the vertex and perpendicular to the base. What is the difference in the areas of the cross sections? Enter your answer in the box.
The difference in the areas of the two triangular cross sections can be found by calculating the area of both triangles.
First, we need to calculate the area of the larger triangle. This triangle has a base of 12 meters (the width of the base of the pyramid) and a height of 10 meters (the height of the pyramid).
Area of larger triangle = (1/2) * base * height
Area of larger triangle = (1/2) * 12 * 10
Area of larger triangle = 60 square meters
Next, we need to calculate the area of the smaller triangle. This triangle has a base of 8 meters (the length of the base of the pyramid) and a height of 10 meters (the height of the pyramid).
Area of smaller triangle = (1/2) * base * height
Area of smaller triangle = (1/2) * 8 * 10
Area of smaller triangle = 40 square meters
Finally, we find the difference in the areas of the two triangles:
Difference = Area of larger triangle - Area of smaller triangle
Difference = 60 - 40
Difference = 20 square meters
Therefore, the difference in the areas of the two triangular cross sections is 20 square meters.