What is the area of this figure?

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m²

Area of figure is 532 m²

Step-by-step explanation:

Consider the figure, It consist of a square ABCD , and two right triangles CDE and DEF.

We have to find the area of the figure

Area of figure = area of square ABCD + area of two right triangles CDE and DEF.

We find the areas separately and then add them,

First area of square ABCD,

Area of square = side × side

Given the side of square = 18 m

Area of square ABCD = 18 × 18 = 324 m²

Area of right angled triangle =

For ΔCDE , base = 18 m and height is 16 m

Area of right angled triangle CDE =

Area of right angled triangle CDE = 144 m².

Similarly, For ΔEDF , base = 8 m and height is 16 m

Area of right angled triangle EDF =

Area of right angled triangle EDF = 64 m².

Thus, Area of figure is 324 + 144 + 64 = 532 m²

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)

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