5. Impact on adding a portion to a given shape

Consider a square whose side length is $6$ $cm$. Let us find the area and perimeter of the square.

Now, let us consider a right-angled triangle of base $6$ $cm$ and height $8$ $cm$ is attached to a rectangle. Find the perimeter and area of the given shape.

 

 

Solution:

 

Given:

 

The length of the rectangle $=9$ $cm$.

 

The breadth of the rectangle $=6$ $cm$.

 

The base of the triangle $=6$ $cm$.

 

The height of the triangle $=8$ $cm$.

 

To find the perimeter and the area of the square after adding a portion to the rectangle.

 

Perimeter of the given shape $=$ Sum of all measures of outer length

 

Perimeter $=(6+9+9+8+10)$ $cm$

 

Perimeter $=42$ $cm$

 

Therefore, the perimeter of the given shape is $42$ $cm$.

 

Area of the given shape $=$ Area of the rectangle $+$ Area of the right triangle

 

Area $=(l \times b)$ $+ \frac{1}{2}(b \times h)$

 

Area $=(9 \times 6) +(\frac{1}{2}(6 \times 8))$

 

Area $=(54)+$ $(\frac{1}{2}\times 48)$

 

Area $=54+24$ $=78$ $sq. cm$

 

Therefore, the area of the given shape is $78$ $sq. \ cm$.