# Finding the Area and Perimeter of a Rectangle

## Area and Perimeter of a Rectangle

The area of a rectangle is found by multiplying the length times the width. The perimeter of the rectangle is found by multiplying 2 times the length, and then adding to that 2 times the width. The reason for that is that the opposite sides of a rectangle are congruent.

If you are trying to find the distance around a rectangle, then you have two sides that have the same length and then two sides that have the same width. If you just multiply 2 times the length and 2 times the width, and add those together, then you’ll find the perimeter of the rectangle. Let’s look at our example.

What is the area and perimeter of a rectangle with a 5ft length and a 3 ft width. We’ve been given a word problem, but we already have this nice picture drawn here of a rectangle. What we can do is we have a 5ft length so we get rid of this l and put that our length is 5ft. Then our width is 3ft, we can get rid of this w and put that our width is 3ft.

Now we’re asked to find area, we should start with our area formula. Area = lw. Area = 5ft × 3ft. The area is 5 times 3 is 15, ft times ft is ft^{2}. Our area is 15ft^{2}. The perimeter. Again, we need to start with our formula. Perimeter is 2 times the length plus 2 times the width. Our perimeter is 2 times, then our length was 5ft. We substitute 5ft for our length plus 2 times, and our width was 3ft. Substitute 3ft for width. P= 2(5ft) + 2(3ft).

Then we need to follow PEMDAS, which means we need to multiply before we add. The perimeter is 2 × 5ft = 10ft, plus 2 × 3ft = 6ft. Finally, we add these together and find the sum. 10ft + 6ft = 16ft. it would be 16ft all the way around our rectangle.