Geometric shapes

There is a wide variety of geometric shapes, which you can read about in detail:

Triangle

Rectangle

Trapezoid

Parallelogram

kite

Rhombus

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Test yourself on triangle!

einstein

Look at rectangle ABCD below.

Side AB is 10 cm long and side BC is 2.5 cm long.

What is the area of the rectangle?
1010102.52.52.5AAABBBCCCDDD

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Geometric shapes

triangle

A triangle is a geometric shape with 33 sides. In every triangle, the sum of angles equals 180180.
Below are the different types of triangles –

  • Equilateral triangle - a triangle in which all sides are equal, all angles are equal, and every height is also a median and an angle bisector.
  • Isosceles triangle - a triangle in which two legs are equal, two base angles are equal, and the median to the base is also the height and the vertex angle bisector.
  • Right triangle - a triangle with one angle of 9090 degrees formed by two legs. The side opposite to the right angle is called the hypotenuse.
  • Scalene triangle - a triangle in which all sides are different from each other.

Examples of right triangles

Rectangle

A rectangle is a quadrilateral with two pairs of parallel opposite sides.
It can also be defined as a parallelogram with a 9090 degree angle.
Since a rectangle is a type of parallelogram, it has all the properties of a parallelogram.

Diagram illustrating a geometric figure ABCD with labeled sides and distinct sections for teaching geometry. The labels include A, B, C, and D, indicating vertices of the figure. Designed for educational purposes in geometry concepts.

Here are the properties of a rectangle:

  • Every pair of opposite sides are equal and parallel.
  • All angles in a rectangle are equal to 9090 degrees.
  • The diagonals of a rectangle are equal to each other.
  • The diagonals of a rectangle bisect each other (divide each other in half, not just intersect).
  • Since both diagonals are equal, all halves of the diagonals are equal.
  • The diagonals of a rectangle are not perpendicular to each other and do not bisect the angles of the rectangle.
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Trapezoid

A general trapezoid is a trapezoid where two of its opposite sides are parallel and are called the bases of the trapezoid.
The other two sides are called the legs of the trapezoid, and they are not parallel and face different directions.

Diagram of a trapezoid labeled with 'Small Base' and 'Large Base,' highlighting its parallel sides. Includes Tutorela branding for educational purposes.


Meet the basic properties of a trapezoid:

• Two sides are parallel to each other
• The sum of the angles that lean on the same leg (one from the small base and the other from the large base) is 180180 degrees.
• If we draw a diagonal that intersects both bases, it will create equal alternate angles between parallel lines.
• The sum of all angles in a trapezoid equals 360360 degrees.
• If we draw a segment that passes exactly through the middle of the 22 legs of the trapezoid, we obtain a segment that is parallel to the bases and equal to half their sum.

Parallelogram

A parallelogram is a quadrilateral with 22 pairs of parallel sides.
How to prove a parallelogram:

  • First way:
    If in a quadrilateral every pair of opposite sides are parallel to each other, the quadrilateral is a parallelogram.
  • Second way:
    If in a quadrilateral every pair of opposite sides are equal to each other, the quadrilateral is a parallelogram.
  • Third way:
    If in a quadrilateral there is one pair of opposite sides that are both equal and parallel, the quadrilateral is a parallelogram.
  • Fourth way:
    If in a quadrilateral, the diagonals bisect each other, the quadrilateral is a parallelogram.
  • Fifth way:
    If in a quadrilateral there are two pairs of equal opposite angles, the quadrilateral is a parallelogram.

Parallelogram

Do you know what the answer is?

kite

A kite is a quadrilateral with two pairs of adjacent equal sides.
To better understand this, imagine that a kite is composed of two isosceles triangles joined together.

Geometric diagram of a kite featuring two overlapping triangles with highlighted segments in orange and blue, representing symmetry or proportional relationships for educational purposes. Includes Tutorela branding.


Here are the main properties of the kite:
The main diagonal in a kite, which extends from the two vertices of the triangles, is both an angle bisector, a median, and perpendicular to the secondary diagonal, which extends from the base angles of the triangles.
Click here to learn more about kites.

rhombus

A rhombus is a parallelogram with a pair of adjacent sides that are equal.
Here are the properties of a rhombus:

Rhombus

  • In a rhombus, all sides are equal.
  • In a rhombus, there are two pairs of parallel opposite sides.
  • In a rhombus, adjacent angles sum to 180180 degrees.
  • The sum of angles is 360360 degrees.
  • In a rhombus, there are two pairs of equal opposite angles.
Check your understanding

Examples with solutions for Triangle

Exercise #1

ABDC is a deltoid.

AB = BD

DC = CA

AD = 12 cm

CB = 16 cm

Calculate the area of the deltoid.

161616121212CCCAAABBBDDD

Video Solution

Step-by-Step Solution

First, let's recall the formula for the area of a rhombus:

(Diagonal 1 * Diagonal 2) divided by 2

Now we will substitute the known data into the formula, giving us the answer:

(12*16)/2
192/2=
96

Answer

96 cm²

Exercise #2

The trapezoid ABCD is shown below.

AB = 2.5 cm

DC = 4 cm

Height (h) = 6 cm

Calculate the area of the trapezoid.

2.52.52.5444h=6h=6h=6AAABBBCCCDDD

Video Solution

Step-by-Step Solution

First, let's remind ourselves of the formula for the area of a trapezoid:

A=(Base + Base) h2 A=\frac{\left(Base\text{ }+\text{ Base}\right)\text{ h}}{2}

We substitute the given values into the formula:

(2.5+4)*6 =
6.5*6=
39/2 = 
19.5

Answer

1912 19\frac{1}{2}

Exercise #3

The trapezoid ABCD is shown below.

Base AB = 6 cm

Base DC = 10 cm

Height (h) = 5 cm

Calculate the area of the trapezoid.

666101010h=5h=5h=5AAABBBCCCDDD

Video Solution

Step-by-Step Solution

First, we need to remind ourselves of how to work out the area of a trapezoid:

Formula for calculating trapezoid area

Now let's substitute the given data into the formula:

(10+6)*5 =
2

Let's start with the upper part of the equation:

16*5 = 80

80/2 = 40

Answer

40 cm²

Exercise #4

Shown below is the deltoid ABCD.

The diagonal AC is 8 cm long.

The area of the deltoid is 32 cm².

Calculate the diagonal DB.

S=32S=32S=32888AAABBBCCCDDD

Video Solution

Step-by-Step Solution

First, we recall the formula for the area of a kite: multiply the lengths of the diagonals by each other and divide the product by 2.

We substitute the known data into the formula:

 8DB2=32 \frac{8\cdot DB}{2}=32

We reduce the 8 and the 2:

4DB=32 4DB=32

Divide by 4

DB=8 DB=8

Answer

8 cm

Exercise #5

Given the trapezoid:

999121212555AAABBBCCCDDDEEE

What is the area?

Video Solution

Step-by-Step Solution

Formula for the area of a trapezoid:

(base+base)2×altura \frac{(base+base)}{2}\times altura

We substitute the data into the formula and solve:

9+122×5=212×5=1052=52.5 \frac{9+12}{2}\times5=\frac{21}{2}\times5=\frac{105}{2}=52.5

Answer

52.5

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