Chapter 11.3, Problem 14PSC

To determine

To Calculate: Total area of the given figure.

Answer to Problem 14PSC

The total area of the given figure is $300$ square units.

Explanation of Solution

Given information:

There are four regions in the figure which are of equal heights. The triangle and the trapezoid are isosceles, and each side of the trapezoid is parallel to a side of the triangle.

Formula used:

Here, we are using the formula

Area of trapezoid = $\frac{1}{2}\left(a+b\right)h$

(here, “ a ” is upper base, “ b ” is lower base and “ h ” is height)

Calculation:

  

Here, $h_1=h_2=h_3=h_4=6$ (given)

And for rectangle length is $20$

Let area of rectangle FHGI be $A_1$

Area of rectangle = $length\times breadth$

  $A_1=6\times 20=120$

Now, let area of trapezium DFEG be $A_2$

Upper base = $10$ and lower base = $20$

Area of trapezoid = $\frac{1}{2}\left(a+b\right)\times h$

(here, “ a ” is upper base, “ b ” is lower base and “ h ” is height)

Hence, $A_2=\frac{1}{2}\left(20+10\right)\times 3$

  $A_2=90$

Now, let area of rectangle BDEC be $A_3$

Area of rectangle = $length\times breadth$

  $A_3=10\times 6=60$

Now, let area of triangle be $A_4$

Area of triangle = $\frac{1}{2}\times base\times height$

  $A_4=\frac{1}{2}\times 10\times 6$

  $A_4=30$

Now, Total area = $A_1+A_2+A_3+A_4$

→ $120+90+60+30$

→ $300$

Conclusion: Hence,the total area of the given figure is $300$ square units.