Question

find the area of each shaded region


PLEASE HELP ​

Answer 1

Given :-

• Find the area of the shaded region?

Solution :-

• First of all, consider the whole figure. It is a rectangle. Let us find the area of the rectangle i.e whole figure first. We know,

       Area of rectangle = length × breadth  

    ⇒ Area = 160 × 100   (Here length = AE + ED = 160 cm & breadth DC=100)

    ⇒ Area = 16000 cm²     ------------- (1)

• Now, we can observe that we cannot directly find the area of the shaded region. So, we should find the area of the unshaded region and subtract it from the total area of the figure to obtain the required answer. We can observe that there are three unshaded triangular regions.(All three are right angled triangles). Let us find their areas one by one.
• First, consider ΔAEF. If AE = 60 cm is the base, AF = 50 cm is the height. We know,

       Area of triangle = 1/2 × b × h

      ⇒ Area of ΔAEF = 1/2 × 60 × 50 = 1500 cm²  ---------- (2)

• Similarly , area of ΔDCG = 1/2 × 100 × 130 = 6500 cm² -------- (3)
• Also, area of ΔFBG = 1/2 × 50 × 30 = 750 cm² ----------- (4)
• Now, we know that, the area of shaded region = area of total figure - area of unshaded region

     ⇒ Area of shaded region = 16000 - (1500 + 6500 + 750)

     ⇒ Area of shaded region = 16000 - 8750 = 7250 cm²

∴ Area of shaded region is 7250 cm²!

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→Sathvik :)