Question

grade 6 unit 4
georgia’s k-12 mathematics standards
date:
the algebra of magic diagnostic assessment
d the value of each of the shapes.
$\blacktriangledown=2$ \\ $\black月牙=\square$ \\ $\blacksquare=3$
(there is another image below with a circle containing 22 and some shapes, and partial text at the bottom: $\blacklozenge=?$ etc.)

Explanation:

Step1: Calculate total value of triangles

We know $\blacktriangledown=2$, and there are 4 triangles.
$4 \times 2 = 8$

Step2: Set up equation for first balance

The left side (4 triangles) equals the right side ($\text{moon} + \square$), and $\square=3$.
$8 = \text{moon} + 3$

Step3: Solve for moon value

Rearrange to isolate the moon value.
$\text{moon} = 8 - 3 = 5$

Step4: Calculate known values for second balance

We know $\blacktriangledown=2$, $\lozenge=2$. Left branch has 3 triangles + 1 diamond: $3 \times 2 + 2 = 8$.

Step5: Find value of right branch total

Total top value is 22, so right branch total is $22 - 8 = 14$.

Step6: Solve for trapezoid value

Right branch has 2 triangles + 1 trapezoid: $2 \times 2 + \text{trapezoid} = 14$
$4 + \text{trapezoid} = 14$
$\text{trapezoid} = 14 - 4 = 10$

Answer:

First problem: $\text{moon} = 5$
Second problem: $\text{trapezoid} = 10$