Quadrangles

The geometry of quadrilaterals

The perimeter of a quadrilateral

Squares and rectangles

Other quadrilaterals

# Squares and rectangles

Two opposite sides of a square are 6 m long. What is its area?

Maria is repainting a stable. She starts with the doors which she is painting black. Each door is in the shape of a rectangle. To calculate how much paint she needs, Maria has to calculate the area or the surface of the doors. Maria takes out a note pad and draws a sketch.

The doors are two and a quarter meters tall, and together they are four meters wide. Maria draws straight lines at every whole meter to be able to calculate how many square meters the doors are. It is one, two, three, four, five, six, seven, eight whole square meters and a few more at the top that are not complete. It's not clear, Maria wants to know exactly how much paint is needed so she has to calculate it. To calculate the area of the stable doors, Maria multiplies the width by the height. Except in geometry, you do not say the width, here it's called the base and it equals four meters.

The height is called height geometry as well, it is two point two five meters. And four times two point two five equals nine square meters. The area of the doors is nine square meters. Look at the units, and with a slightly raise two meter raised to the power of two or meter squared. This is the area you get when you multiply a base and a height measured in meters.

If Maria had measured the base and the height in centimeters, the answer would have been in centimeters squared. Now, Maria is going to measure this table wall as well, and she starts with the lower part. It is five meters wide and up to the ceiling, it's also five meters. It's a square. Since squares also are rectangles, you get the area by taking the base times the height, five meters tall and five meters wide - five times five. The wall is 25 meters squared.

But since the base and the height in a square are equal, you can do like this as well: any side times itself. In other words, the side squared. But wait a minute, the whole wall should not be read, the door takes up a part of the surface. So Maria takes the wall's area - 25 square meters - minus the door's area - 9 square meters - that equals 16 square meters. There are other parts on the wall, but they're not squares or rectangles, so we'll count them another time. The area of a rectangle equals the base times the height.

Measure the base and the height in the same units and get the answer in those units squared. You get a square's area if you take a side of the square and multiply it by itself. One meter times one meter equals one meter squared.