Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
A tent is a tetrahedron with the corners , , and , with lengths in metres. The cloth of the face lies on the ground. Find the volume of air inside the tent. Then find the area of the face , and with it the height of the corner above the ground face.
is the determinant of the three vectors. The parallelepiped has volume and the tetrahedron has of that. The product is zero when the vectors are coplanar.
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. The edges. , and .
Step 2. The volume. The determinant is . The volume is cubic metres.
Step 3. The base. with size . The area of is square metres.
Step 4. The height. , so metres.
Answer: about cubic metres, and a height of about metres.
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