Question

1. brandon sketched two signs on a coordinate plane. each gridline represents 1 inch. which of the following statements are true about the signs? select all that apply.

the area of the vote today sign is 30 in².
brandon can find the area of the eco team meeting sign by using the equation area = (5 in. × 5 in.) × 2.
the area of the eco team meeting sign is 50 in².
brandon can find the area of the vote today sign by using the equation area = (3 in. × 5 in.) × 2.
the two signs require the same amount of material.
the area of the eco team meeting sign is smaller than the area of the vote today sign.

1. jada and kyle have another irregular shaped package to design. this irregular polygon will be the base of the new package. find the area of this irregular polygon. enter your answer as a decimal to the tenths place if necessary.

the area of the polygon is ______ in².

Explanation:

Problem 3

Step1: Analyze Vote Today sign

The "Vote Today" sign is a regular hexagon, which can be split into 2 congruent trapezoids. Each trapezoid has bases $b_1=5$ in, $b_2=3$ in, height $h=5$ in.
Area of 1 trapezoid: $\frac{(5+3)}{2} \times 5 = 20$ in²
Total area: $20 \times 2 = 40$ in²

Step2: Analyze Eco Team sign

The "Eco Team" sign is a regular hexagon, split into 2 congruent trapezoids. Each trapezoid has bases $b_1=5$ in, $b_2=3$ in, height $h=5$ in.
Area of 1 trapezoid: $\frac{(5+3)}{2} \times 5 = 20$ in²
Total area: $20 \times 2 = 40$ in²

Step3: Verify each statement

1. "Area of Vote Today is 30 in²": False (actual 40 in²)
2. "Area = (5×5)×2 for Eco Team": False (incorrect formula)
3. "Area of Eco Team is 50 in²": False (actual 40 in²)
4. "Area = (3×5)×2 for Vote Today": False (incorrect formula)
5. "Two signs need same material": True (both 40 in²)
6. "Eco Team area is smaller": False (areas are equal)

Step1: Split polygon into shapes

Divide the irregular polygon into a rectangle and two triangles:

1. Rectangle with vertices $(-10,7), (6,7), (6,-5), (-10,-5)$
2. Triangle 1: $(-10,-5), (-4,0), (-1,-5)$
3. Triangle 2: Remove the overlapping triangle area (since the polygon is the rectangle minus this triangle)

Step2: Calculate rectangle area

Length $l = 6 - (-10) = 16$ in, width $w = 7 - (-5) = 12$ in
Area: $16 \times 12 = 192$ in²

Step3: Calculate triangle area

Triangle has base $b = -1 - (-10) = 9$ in, height $h = 0 - (-5) = 5$ in
Area: $\frac{1}{2} \times 9 \times 5 = 22.5$ in²

Step4: Find polygon area

Subtract triangle area from rectangle area: $192 - 22.5 = 169.5$ in²

Answer:

• The two signs require the same amount of material.

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Problem 4