Square Inscribed in a Triangle

Introduction:

Geometry is one of the parts in mathematics. Square inscribed in a triangle means the square presents inside a triangle. With this the area of the square can be found out easily. The area of the part which is in triangle but not in square can also be calculated. The sided of the square is in base of the triangle.


Example Diagrams – Square Inscribed in a Triangle:

 

 
Formula involved:

Side of the square = `"Base - Height" / "Base + Height"`


Example Problems – Square Inscribed in a Triangle:

Example 1 – Square inscribed in a triangle:

Find the area of a shaded area from the following figure:
 

Solution:

Given that the side of the square is 4cm.

The length of base of a triangle is 7cm and the height is 10cm.

The formula to find the required shaded portion is = Area of triangle – Area of square

= `1/ 2` `*` base `*` height - side2

= `1/ 2` `*` 7 `*` 10 – 42

= 35 – 16

= 19cm2

Example 2 – Square inscribed in a triangle:

Find the area of a shaded area from the following figure:
 

Solution:

Given that the side of the square is 3cm.

The length of base of a triangle is 6cm and the height is 9cm.

The formula to find the required shaded portion is = Area of triangle – Area of square

= `1/ 2` `*` base `*` height - side2

= `1/ 2` `*` 6 `*` 9 – 32

= 29 – 9

= 18cm2   

Example 3 – Square inscribed in a triangle:

Find the area of a shaded area from the following figure:
 

Solution:

Given that the side of the square is 2cm.

The length of base of a triangle is 4cm and the height is 6cm.

The formula to find the required shaded portion is="Area" of triangle – Area of square

= `1/ 2` `*` base `*` height - side2

= `1/ 2` `*` 4 `*` 6 – 22

= 12 – 4

= 8 cm