Question

What is the area of this figure?

Answer 1

In the given composite figure:

Labelled the figure:

In a square ABCD figure:

Each side is of 18 m each

Area of a square is given by:

`\text{Area of square} = (\text{Side})^2`

Then;

`\text{Area of square ABCD} = (18)^2 = 324 m^2`

Now, In right angle triangle CEF:

Area of a right angle triangle is given by:

`\text{Area of triangle} = (1)/(2)(\text{Base}) \cdot (\text{Height})`

In a a triangle CEF:

Base = CE = 8 m and Height = CF = 16 m

then;

`\text{Area of triangle CEF} = (1)/(2)(8) \cdot (16)=4 \cdot 16 = 64 m^2`

Similarly in triangle DCF:-

Base = CD = 18 m

Height = CF = 16 m

then;

`\text{Area of triangle DCF} = (1)/(2)(18) \cdot (16)=9 \cdot 16 = 144 m^2`

Thus:

area of composite figure =Area of square ABCD + Area of triangle CEF + Area of triangle DCF

Area of this composite figure= 324 +64+144 = 532 square meter.

Therefore, area of this figure is 532 meter square.