Calculate Rectangle Area: Given Perimeter 30cm and Height 5cm

Question

Look at the rectangle in the figure.

Its perimeter is 30 cm.

What is its area?

00:05 Let's find the area of rectangle A, B, C, D.

00:10 The perimeter is found by adding up all the sides of the rectangle.

00:17 Remember, in a rectangle, opposite sides are equal.

00:24 Plug in the values you have into the formula to find the lengths of the sides.

00:29 We've arranged the equation to have all unknowns on one side.

00:37 This gives us the lengths of sides A, B and D, C.

00:42 Now, let's use the formula to calculate the rectangle's area.

00:48 Insert the known values and solve to find the area. And that's it!

The perimeter of the rectangle equals the sum of all its sides, which means:

$P=AB+BC+CD+DA$

Since in a rectangle each pair of opposite sides are equal, we can say that:

$BC=AD=5$

This means that the two sides together equal 10, and now we'll subtract them from the perimeter and get:

$AB+DC=30-10=20$

This means sides AB and DC together equal 20, and since they are equal to each other, we'll divide 20 to find out how much each one equals:

$20:2=10$

Now we'll multiply side AB by side BC to find the area of the rectangle:

$10\times5=50$

50 cm²