Pressure, Force and Area

Use pressure = force ÷ area.

So $1000\text{ N}÷0.5{\text{ m}}^2=2000{\text{ N/m}}^2$.

Dividing by 0.5 is the same as multiplying by 2, so the answer is bigger than 1000, not smaller: spreading 1000 N over only half a square metre gives 2000 N on every square metre.

The pressure is 2000 N/m².

Rearrange pressure = force ÷ area to get force = pressure × area.

So $900{\text{ N/m}}^2\times 2{\text{ m}}^2=1800\text{ N}$.

Each square metre carries 900 N, and there are 2 square metres, so the total force is 1800 N.

Use area = force ÷ pressure.

So $1800\text{ N}÷1200{\text{ N/m}}^2=1.5{\text{ m}}^2$.

The area is $1.5{\text{m}}^2$.

First find the area of the base. For a rectangle, area = length × width $=1.5\text{ m}\times 0.6\text{ m}=0.9{\text{ m}}^2$.

Then use pressure = force ÷ area. So $1350\text{ N}÷0.9{\text{ m}}^2=1500{\text{ N/m}}^2$.

The pressure is 1500 N/m².

Check three things: $1.5\times 0.6=0.9$, not 9; the force must be divided by the area ($0.9{\text{m}}^2$), not by a single side length; and because you are dividing by a number smaller than 1, the answer is bigger than 1350, not smaller.

First find the area of the slab. For a square, area = side × side $=0.5\text{ m}\times 0.5\text{ m}=0.25{\text{ m}}^2$.

Then use force = pressure × area. So $2000{\text{ N/m}}^2\times 0.25{\text{ m}}^2=500\text{ N}$.

The force is 500 N.

Take care to multiply by the area ($0.25{\text{m}}^2$), not by a side length ($0.5\text{m}$) and not by the perimeter ($2\text{m}$), and to multiply rather than divide, since force = pressure × area.

First find the area of the base using area = force ÷ pressure. So $800\text{ N}÷3200{\text{ N/m}}^2=0.25{\text{ m}}^2$.

For a square base, area = side × side, so the side is the square root of the area: $\sqrt{0.25}=0.5\text{ m}$.

The side length is $0.5\text{m}$.

Three steps are easy to get wrong: stopping at the area ($0.25{\text{m}}^2$) instead of square rooting it, squaring the area instead of rooting it ($0.25^2=0.0625$), and dividing the wrong way round ($3200÷800=4$, which would give a side of $2\text{m}$).