The area of the entire trapezoid is 48. What is the area of the shaded region? 

Trapezoid area = 1/2 (a+b) × h 48 = 1/2 (8 + 4X) 4 48 = 2 (8 + 4X) 48 = 16 + 8X 32/8 = X X = 4 Shaded area left = 1/2 × 8 × 4 = 16 Shaded area right = 1/2 × 4 × 4 = 8 Total shaded area = 16 + 8 = 24

Greetings. Since the area of the entire trapezoid is 48 square units and we know that the area of a trapezoid is 1/2(a+b)h. We will simply substitute the values for a, b, and h to get 1/2(8+4X) times 4. That is =2(8+4X)=16+8x. This area is equal to 48. Therefore, 16+8X=48, and 8X=48-16=32, and X=4. Now that we know the value of X, we can use this value to determine the area of the small trapezoid and thereafter subtract this value from the value of the bigger trapezoid to find the combined areas of the shaded portions. The area of the small trapezoid is 1/2(8+4) times 4= 1/2(12)×4 =6×4= 24 square units. Finally, the area of the shaded portions is (48-24)=24 square units. Lovely.

Interesting, this is one I've forgotten. Thanks for another thought provoking maths problem.

The shaded area is 24.

I couldn't remember the formula for a trapezoid but got the answer by dividing the center section into two triangles and working from there.

X = 8/2 = 4 three 4x4 squares =48 1sq = 16 1/2 square = triangle = 8 this trapzd = 6 equal triangles (4x4x5.657) Shaded = unshaded= 3 tri each 3 x 8 = 24 shaded (or unshaded)

The answer can also be calculated using the formula for the area of a triangle.

lots of little calcs but i got it. thanks

Sir How to find the centeriod of Triangle

Unfortunately....Trapezoid - UK definition:a flat shape with four sides, none of which are parallel. US definition:a flat shape with four sides, where two of the sides are parallel

24 units^2

Since I don't own a trapezoid farm what is my motivation for solving this

The area just has blue lines in it, it's not technically shaded.

A=24 UNITS square

For us color blind people … what blue lines

24

You need to do a better job with these drawings. Some of us dont watch the video until we solve the puzzle. The base of the triangle on the right looks larger than x which makes this problem impossible to solve without knowing the angle.