Question

To the nearest square unit, what is the area of the shaded region?

Answer 1

Since the diagram is a regular octagon, it can form 8 of the same triangles.
The area of one triangle= 1/2 x 15 x 18.11
=135.825
The area of the octagon = 135.825 x 8
= 1086.6
The area of shaded region will be the area of the octagon minus the square
The area of the shaded region = 1086.5-(15x15)
=861.6
Answer will be C as you need to round off to three significant figures

Answer 2

First we need to distribute it in parts of
2 trapezium
1 rectangle 
These reading are for shaded region
Each side of octagone is 15 as it is regular
The height of octagone=18.11 x 2=36.22 this is one side of trapezium
and the other is 15  as it is regular
the height of trapezium=10.61 from the whole horizontal length is equal to vertical as it is regular octagone 
then we need to subtract this horizontal length by 15 which is one of the side =36.22-15=21.22 then divide it by 2 so that can get height of each trapezium =10.61
so the area of each trapezium= 0.5 x (36.22+15) x 10.61=271.7
And of two are= 271.7 x 2 =543.4
The area of triangle = 15 x 21.22 ( this is not the area of rectangle shown it is the area of rectangle which is above it and part of shaded region.
=318.3 
Area of shaded region = 543.44 + 318 3 =861.7=862 to nearest whole number
SO ANSWER IS C THAT IS 862 square units