In this worksheet, we will practice using the properties of parallel and perpendicular planes to solve problems.

**Q1: **

and are two parallel planes, where is a point between the two planes. Two straight lines are drawn from the point such that one intersects the planes and at points and respectively, and the other intersects the planes and at points and respectively. If and the surface area of , find the surface area of .

- A
300 cm
^{2} - B
150 cm
^{2} - C
1βββ350
cm
^{2} - D
50 cm
^{2}

**Q2: **

and are two parallel planes, and , , and are drawn to intersect the plane at the points , , and , respectively, and the plane at the points , , and , respectively, where the point doesnβt belong to any of the planes. Given that , , , and , determine the area of the .

**Q3: **

Given that the plane is parallel to the plane , find the values of and .

- A ,
- B ,
- C ,
- D ,

**Q4: **

, , and are three parallel planes intersected by two coplanar straight lines and , where . If , find the length of .

**Q5: **

, , and are three parallel planes intersected by two coplanar straight lines and such that . If , find the length of .

**Q6: **

Given that the plane is perpendicular to the plane , find the value of .

**Q7: **

Two 3D shapes lie between two parallel planes. Any other plane which is parallel to the two planes intersects both shapes in regions of the same area. What can you deduce about the shapes?

- AThey have the same surface area.
- BThey are both prisms.
- CThey are congruent.
- DThey have the same volume.
- EThey are similar.