**Question 1: **

What is the area of the different cross sections of the following rectangular prism?

image

**Solution:**

We have $3$ different pairs of bases so we should get $3$ different cross sections in this case.

If we cut the prism by a plane parallel to the base then we will get a rectangle with sides of length $6$ cm and $5$ cm.

So, area of the cross section when cut by a plane parallel to the base will be:

Area $(A)$ = $6 cm \times 5 cm$ = $30 cm^2$

If we cut the prism by a plane perpendicular to the base then we will get a rectangle of side lengths $11$ cm by $5$ cm.

So, area of the cross section when cut by a plane perpendicular to the base will be:

Area $(A)$ = $11 cm \times 5 cm$ = $55 cm^2$

If we cut the prism by a plane across the top then we will get a rectangle of side lengths $11$ cm and $6$ cm.

So, area of the cross section when cut by a plane across the top of the prism will be:

Area $(A)$ = $11 cm \times 6 cm$ = $66 cm^2$

**Question 2: **

Find the area of the cross section of the following figure?

image

**Solution:**

We can see that the cross section is a rectangle.

If we cut the given prism horizontally then the length and width remains the same.

So, area of the cross section of the given figure will be:

Area $(A)$ = $5 \times 3$ = $15\ units^2$

**Question 3:**

Describe the shape resulting from the following cross section.

a) image

**Solution:**

Here, we can see that the rectangular prism is cut horizontally by a plane. Hence, we get the resulting cross sectional shape as a rectangle.

b) image

**Solution: **

Here, we can see that the rectangular prism is cut vertically by a plane. Hence, we get the resulting cross sectional shape as a rectangle.