A rectangular pyramid has a height of 8 meters. The base measures 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-sections?

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step-by-step explanation:

18 units²

step-by-step explanation:

first let's find altitude bd using the distance formula

d = √((y₂ - y₁)² + (x₂ - x₁)²)

bd = √((0 - -3)² + (0 - 3)²)

bd = √18

given the placement of points a and c, we can denote that point d bisects segment ac.

we will call ac the base.

using the distance formula

ac = √((0 - 6)² + (-6 - 0)²)

ac = √72

knowing our base and our height, we can plug these into our triangle area formula

area = (b * h)/2

area = (√18 * √72) / 2

area = (√1296) / 2

area = 36 / 2

area = 18 units²

the furthest the dog can be is 508 meters away from the house, and the closest he can be is 492 meters away from the house.