Area Maze Math Puzzle | Find the Area of Rectangle

Geometry math problem: Find the area of rectangle from the area maze math puzzle

This puzzle is made with inspiration from Japanese puzzle creator Naoki Inaba

Find the value of the question mark in the following diagrams (Area of the shaded rectangle).

Solution

To solve this puzzle, we can name the figure

Let MN = x and FG = y, then

MY = XF

⇒ MN + NY = XE + FE

⇒ x + 2 = 2 + FE

so, FE = x

MX = FY

⇒ XL + LM = FG + GY

⇒ 2 + LM = y + 3

so, LM = y + 1

Area of the shaded rectangle = XM × MY

Now extent CN and AL then they meet at D. and form rectangle ABCD and rectangle MNDL

Area of the rectangle ABCD = AB × BC = 8 × 7 = 56 cm²

Area of the rectangle MNDL = Area of the rectangle ABCD − Area of ABCNML

⇒ Area of the rectangle MNDL = 56 − 36 = 20 cm²

Also we have, Area of the rectangle MNDL = MN × ML = x( y + 1)

⇒ x( y + 1) = 20

⇒ xy + x = 20……………………………………….eq(1)

Now extent CN and AL then they meet at D. and form rectangle PQRS and rectangle EFGS

Area of the rectangle PQRS = PQ × QR = 7 × 6 = 42 cm²

Area of the rectangle EFGS = Area of the rectangle PQRS − Area of PQRGFE

⇒ Area of the rectangle EFGS = 42 − 26 = 16 cm²

Also, we have, Area of the rectangle EFGS = EF × GF = xy

⇒ xy = 16……………………………………….eq(2)

Now we need to solve the equation system 1 and 2

That is from equation (1) & equation (2)

xy + x = 20

⇒ 16 + x = 20

⇒ x = 4 cm ⇒ y = 4 cm

Area of the grey rectangle = XM × MY = (y + 3) × (x + 2)

⇒ Area of the shaded rectangle = 7 × 6

so we got the solution to this area maze math puzzle as

Area of the shaded rectangle = 42 cm²