Question

What is the area of this polygon?

A = 400 cm²

A = 338 cm²

A = 316 cm²

A = 238 cm²

Answer 1

316 cm²

A polygon is given to us and we are interested in finding out the area of the polygon .

• Here we can see that the polygon is made up of a rectangle and a triangle .

We can separately find out their areas and then add them up to find out the area of the polygon.

So that ,

`\sf\longrightarrow Area = ar(\triangle)+ ar(\blacksquare) \\`

• We know that the area of rectangle is length × breadth and that of triangle is 1/2 × base × height . So ,

`\sf\longrightarrow Area = (1)/(2)(base)(height) + (length)(breadth) \\`

• Here height of triangle can be calculated by subtracting the lengths 18cm and 14cm and its base can be calculated by subtracting CD from BD ( see figure in attachment.)

`\sf\longrightarrow Area = (1)/(2)(4cm)(11cm)+(21cm)(14cm)\\`

`\sf\longrightarrow Area = 22cm^2 + 294cm^2\\`

`\sf\longrightarrow \underline{\boxed{\bf Area_((polygon))= 316cm^2}} \\`