What is the area of this polygon? A = 400 cm² A = 338 cm² A = 316 cm² A = 238 cm²

Question

asked Apr 18, 2023 22.2k views

1 Answer

Tek Nath Acharya · Answer 1 · 2023-04-23T02:10:55+0000

316 cm²

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

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.)

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

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

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