Question

there is a balance diagram. on the left side of the balance, there are 5 hexagons and 1 trapezoid (with a cross mark on the trapezoid). on the right side, there are 2 diamonds (each labeled 5) and 1 trapezoid (with a cross mark on the trapezoid). below the diagram, it is given that trapezoid = 1, diamond = 5, and hexagon =? (represented by a blank box).

Explanation:

Step1: Analyze left side weight

Left side has 5 hexagons and 1 trapezoid (value 1). Let hexagon be \( x \), so left weight: \( 5x + 1 \).

Step2: Analyze right side weight

Right side has 2 diamonds (each 5) and 1 trapezoid (1). So right weight: \( 2\times5 + 1 = 10 + 1 = 11 \).

Step3: Set equilibrium equation

Since the scale is balanced, \( 5x + 1 = 11 \). Subtract 1: \( 5x = 10 \). Divide by 5: \( x = 2 \).

Answer:

The value of the hexagon (\( \boldsymbol{\bigcirc} \)) is 2.