Area of Shapes

Before we begin, what is 'area'? What does it mean to calculate area? Please read carefully, as it will help you understand this topic.

When calculating area, we can classify two-dimensional shapes as follows:

Rectangular shapes, each side of which is straight and perpendicular (like squares and rectangles),
Shapes with slanted sides (like triangles, parallelograms, rhombuses, kites, and trapezoids etc.),

Shapes with curved edges, such as circles or ellipses.

Area of Rectangles ( Square and Rectangle )

Find the area of this rectangle.

Calculating the area of a shape means determining how many unit squares can fit into that area.

When we repeat these steps;

There are 10 squares in each row. With 6 rows, that equals 60 square units.

10 cm . 6 cm = 60 cm²

Example:

Let's place unit squares inside the square.

as we proceed with the steps

Let's formulate (generalize) it.

Shapes with slanted sides ( Triangle )

Calculating the edge of a triangle or a shape with an inclined side still relies on the logic of calculating the area of a square and rectangle.

We use the area of a rectangle to find the area of a triangle.

Specifically, we will frequently use the fact that when we divide a rectangular region from corner to corner, we obtain two equal areas.

We calculated how to find the area of right-angled and acute-angled triangles. We will specifically address how to find the area of an obtuse-angled triangle in the topic of how to calculate the area of a triangle.

Area of Quadrilaterals

The area of a triangle and the area of rectangular regions form the basis for calculating the area of other shapes.

*Try to transform unfamiliar shapes into familiar ones (like squares, rectangles, triangles). You can use methods such as breaking them into pieces or cutting and repositioning.

*Know the angle properties of polygons and how their diagonals intersect.

Area of the Rhombus

*Try to transform unfamiliar shapes into familiar ones (like squares, rectangles, triangles).

I can divide the rhombus into triangles.

The fundamental characteristic of a rhombus is that its side lengths are equal, which gives us the properties of an isosceles triangle. That is, a line dropped from the apex of an isosceles triangle bisects and is perpendicular to the base. Click for more information about the isosceles triangle.

let's name the diagonals for which we've indicated the midpoints.

let's find it using the area of the rectangle.

We know that the diagonals are perpendicular to each other. When we multiply the two perpendiculars, we find the area of the rectangle formed by the perpendicularity.

Can you find the area of the deltoid using these methods?

The Area of a Parallelogram

*Try to transform unfamiliar shapes into familiar ones (like squares, rectangles, triangles).

I can divide the paralelogram into triangles.

Method 2

Due to the sides being parallel to each other, the indicated angles are equal to each other (corresponding angles).

If we cut it from the corner to form a right triangle, the cut piece fits perfectly on the other side, because the angles are equal (90 degrees - corresponding angles and the other angle). Also, the sides are equal (height - due to the property of the parallelogram where opposite sides are equal).