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I need help with 7 8 and 9 question perimeter and area

I Need Help With 7 8 And 9 Question Perimeter And Area class=

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The perimeter and area of the equilateral, isosceles and right angled triangle are  16.2mm 12.6mm², 15.2in and 9.61in², 21.47yds and 16.81yds² respectively.

What is the area of the equilateral, isosceles and right angle triangle?

Note that:

The perimeter of an Equilateral triangle is expressed as P = 3a

The area of an Equilateral triangle is expressed as A = ((√3)/4)a²

Where a is the dimension of the side.

The perimeter of an Isosceles triangle is expressed as P = 2a + b

The area of an Isosceles triangle is expressed as A = (ah)/2

Where b is the slant height, a is the dimension of the base and h is the height.

The perimeter of a Right angled triangle is expressed as P = a + b + c

The area of a Right angled triangle is expressed as A = (ab)/2

Where a and b is the dimension of the two sides other than the hypotenuse and c is the hypotenuse.

For the Equilateral triangle.

Given that;

  • a = 5.4mm
  • Perimeter P = ?
  • Area A = ?

Perimeter P = 3a

P = 3 × 5.4mm

P = 16.2mm

Area A = ((√3)/4)(5.4mm)²

A = ((√3)/4)( 29.16mm² )

A = 12.6mm²

The Perimeter and Area of the Equilateral triangle are 16.2mm 12.6mm² respectively.

For the Isosceles triangle.

Given that;

  • Base a = 3.4in
  • Slant height b = 5.9in
  • Perimeter P = ?
  • height h = ?
  • Area A = ?

Perimeter P = 2a + b

P = 2(b) + a

P = 2(5.9in) + 3.4in

P = 11.8in + 3.4in

P = 15.2in

The height h is the imaginary line drawn upward from the center of a.

First, we calculate the height using Pythagorean theorem

x² = y² + z²

Where x = b = 5.9in, y = a/2 = 3.4in/2 = 1.7in, and z = h

(5.9in)² = (1.7in)² + h²

34.81in² = 2.89in² + h²

h² = 34.81in² - 2.89in²

h² = 31.92in²

h = √31.92in²

h = 5.65in

Now, the area will be;

A = (ah)/2

A = (3.4in × 5.65in )/2

A = 19.21in²/2

A = 9.61in²

The Perimeter and Area of the Isosceles triangle are 15.2in and 9.61in² respectively.

For the Right angled triangle.

Given that;

  • a = 8.2yds
  • b = 4.1yds
  • c = 9.17yds
  • Perimeter P = ?
  • Area A = ?

Perimeter P = a + b + c

P = 8.2yds + 4.1yds + 9.17yds

P = 21.47yds

Area A = (ab)/2

A = ( 8.2yds × 4.1yds)/2

A = ( 33.62yds²)/2

A = 16.81yds²

The Perimeter and Area of the Right angled triangle are 21.47yds and 16.81yds² respectively.

Therefore, the perimeter and area of the equilateral, isosceles and right angled triangle are  16.2mm 12.6mm², 15.2in and 9.61in², 21.47yds and 16.81yds² respectively.

Learn more about Pythagorean theorem here: brainly.com/question/343682

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