# Triangle Area

Triangle Area :The area of a polygon is the number of square units inside that polygon. Area is 2-dimensional like a carpet or an area rug. A triangle is a three-sided polygon.In this section, we will study the Area of Triangles, but triangles of several types of triangles such as acute triangle, right triangle, isosceles triangle, equilateral triangle and obtuse triangle .

**Some solved examples**

1) Find the height of an acute triangle whose base is 20 cm and area is 150 cm

^{2}.

**Solution :**

Area = ½ base x height

150 = ½ x 20 x height

150 = 10 x height

∴ height = 150 / 10 = 15 cm.

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2) In a right triangle , if base is 20 m and height is 5 m, find the area of triangle.

**Solution :**

Area = ½ x base x height

A = ½ x 20 x 5

A= 100 / 2

A = 50 m

^{2}

Area = ½ x base x height

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3) Find the area of isosceles right triangle , if one of the equal side is 20 in long.

**Solution :**

In right triangle any one of the two sides which are at right angle can be taken as the base and other side as height.

Area = ½ x 20 x 20

Area = 200 cm

^{2}

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4) Find the area of equilateral triangle with sides 8 cm.

**Solution :**

Area of equilateral triangle = ( √ 3 a

^{2}) / 4

Area = ( √ 3 x 8

^{2}) / 4

Area = ( √ 3 x 64 ) / 4

Triangle Area = 16 √ 3 cm

^{2}

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5) ABCD is a rectangle with dimensions 32 m by 18 m. ADE is a triangle such that EF ⊥ AD and EF = 14 cm. Calculate the area of the shaded region.

**Solution :**

Area of rectangle ABCD = l x w

A = 32 x 18 = 576 m

^{2}

Area of Triangle ADE = ½ x base x height

A = ½ x 18 x 14

A= 126 m

^{2}

Area of shaded region = Area of rectangle ABCD – Area of triangle ADE

A = 576 – 126 = 450 m

^{2}

∴ Area of shaded region = 450 m

^{2}

**Mensuration : Area and Perimeter**

• Perimeter and Area of Irregular Shape

• Area and Perimeter of the Rectangle

• Area of Square (perimeter of square)

• Perimeter of Parallelogram(Area of Parallelogram)

• Area of Rhombus(Perimeter of rhombus)

• Area of Trapezoid (Trapezium)

• Triangle Area (Perimeter of triangle)

• Herons Formula

• Perimeter and Area of Irregular Shape

• Area and Perimeter of the Rectangle

• Area of Square (perimeter of square)

• Perimeter of Parallelogram(Area of Parallelogram)

• Area of Rhombus(Perimeter of rhombus)

• Area of Trapezoid (Trapezium)

• Triangle Area (Perimeter of triangle)

• Herons Formula

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