2 diagonals of this rectangle divide it into 4 triangles. What is area of rectangle if area of the shaded region is 42?

Question

The 2 diagonals of this rectangle divide it into 4 triangles.

If the area of the shaded region is 42, then what is the area of the rectangle?

Answer 1

56

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Add 2 lines to divide the rectangle to 8 triangles.
All of them are equal as have same sides. See attached picture.
Shaded region contains 6 triangles ---> 42/6=7 area of one triangle
7*8=56 area of rectangle

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Answer 2

Let a and b be the sides of the rectangle.
We can calculate the area of the shaded area as follows:
( a x b) / 2 + (a x b) /4 = 42
Let the first term of the equation be equal to X, and the second term be equal to X/2
We can write the above equation, as follows:
X + X/2 = 42 Solving the equation, it gives X = 28
Then the area of the rectangle is 28 x 2 = 56

Answer 3

Area Of rectangle =56