Answer:
Area = 4ab - 2(ab-b^2) - ab - ab
simplified version: 2ab -2(ab-b^2)
Explanation:
- instead of finding the area of shaded region, we can take a different appraoch. We can subtract the non-shaded region from the overall rectangle because white triangles are easier to measure.
area of rectangle is = length * base
= 2b * 2a
=4ab
1. Area of Left white triangle = 1/2 (base)(height)
=1/2 (2a-2b)(2b)
=1/2 (4ab-4b^2)
=1/2 4(ab-b^2)
=2(ab-b^2)
2. Area of bottom right triangle= 1/2 (base)(height)
=1/2 (2a)(b)
=ab
3. Area of Top Right triangle: 1/2 (base)(height)
=1/2 (2b-b)(2a)
=1/2 (b)(2a)
=ab
Area of grey triangle = area of rectangle - area of triangle 1 - area of triangle 2 - area of triangle 3
Area = 4ab - 2(ab-b^2) - ab - ab
Area = 4ab -2(ab-b^2) - 2ab
Area = 4ab - 2ab -2(ab-b^2)
Area = 2ab -2(ab-b^2)