Area of Triangle

Triangle is polygon ( a plane shape that have three or more straight sides) with three angles and three sides( One of the lines that make a flat (2-dimensional) shape. Or one of the surfaces that make a solid (3-dimensional) object). There are three special names given to triangles that tell how many sides (or angles) are equal. There can be 3, 2 or no equal sides/angles:

Various kinds of triangles according to angle.

• Acute triangle . The third large angle of less than 90 °.
• Right triangle. One large angle of 90 °.
• Obtuse triangle. Big one corner more than 90 ° and less than 180 °

Various kinds of triangles according to the side.

• Scalene triangle, three sides of unequal length.
• Isosceles triangle, two sides equal in length.
• Equilateral triangle, three sides equal in length.

Equilateral Triangle =    Three equal sides  Three equal angles, always 60°

Isosceles Triangle = Two equal sides   Two equal angles

Scalene  Triangle = No equal sides   No equal angles

The characteristics of the triangle

• Triangles have three sides.
• Vertex of the triangle there are 3
• The whole  angles of triangle is 180 °.

Area of triangle

Area = ½ x b x h ( b=base, h=height)

Example :
Base of triangle : 15 cm and height : 12 cm
Area = ½ × b × h
         = ½ × 15 × 12
         = 90 cm

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Area of Rhombus

A rhombus is a four-sided shape where all sides have equal length. Also opposite sides are parallel and opposite angles are equal. Another interesting thing is that the diagonals (dashed lines in second figure) of a rhombus bisect each other at right angles. Rhombus formed from an isosceles triangle and its shadow reflected on the base as the axis of symmetry. Isosceles triangle ABC is reflected to the side of the base AC, so it appears his shadow ACD. ACD is congruent with the ABC. 

The properties of a rhombus as follows :

1. The length of its four sides equal in length 

     and Opposite sides are parallel.

• AB = BC = CD = AD
• AB // DC dan AD // BC

2. Both rhombus diagonal bisect each other 

    the same length and intersect 

    perpendicularly.

3. Opposite angles equal.

• ∠BAD =  ∠BCD
• ∠ABC =  ∠ADC
• ∠BAE =  ∠DAE =  ∠BCE = ∠ DCE
• ∠ADE =  ∠CDE =  ∠ABE =  ∠CBE

4. Both diagonal are  axis of symmetry.

• Diagonal AC ┘└ BD
• Panjang AE = EC
• Panjang DE = EB

Area of Rhombus :

Area =  ½ x d1 x d2
Based on rhombus area can be found each diagonal.

• d1  = 2A/d2
• d2 = 2A/d1

Example :

1. A rhombus has diagonal 1 = 15 cm and diagonal 2 = 20 cm. What is the area ?

    Area = di x d2

             = 15 x 20

             = 300 cm

2. A rhombus has 300 cm area and one of the diagonal is 30 cm. What is the other diagonal ?

     d1 = 2A/d2

          = 2(300)/30

          = 600/30

          = 20 cm

3.  A rhombus has 187 cm area and one of the diagonal is 17 cm. What is the other diagonal ?

     d2 = 2A/d1

          = 2(187)/17

          = 374/17

          = 22 cm

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