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$Mary is making a decorative yard space with dimensions as shaded in green ( /_\OAB). Mary would like to cover the yard space with artificial turf (plastic grass-like rug). Mary reasoned that she could draw a rectangle around the figure so that the point O was at a vertex of the rectangle and that points A and B were on sides of the rectangle. Then she reasoned that the three smaller triangles resulting could be subtracted from the area of the rectangle. Mary determined that she would need 28 square meters of artificial turf to cover the green shaded yard space pictured exactly. Is Mary's reasoning and claim correct? What is the correct evidence? Be sure to have all three parts of a CER answer: make a claim, provide evidence, and explain your reasoning for full credit.$

Mary is making a decorative yard space with dimensions as shaded in green ( $\triangle \mathrm{OAB})$ . $\newline$ Mary would like to cover the yard space with artificial turf (plastic grass-like rug). $\newline$ Mary reasoned that she could draw a rectangle around the figure so that the point $O$ was at a vertex of the rectangle and that points $A$ and $B$ were on sides of the rectangle. Then she reasoned that the three smaller triangles resulting could be subtracted from the area of the rectangle. Mary determined that she would need $28$ square meters of artificial turf to cover the green shaded yard space pictured exactly. $\newline$ Is Mary's reasoning and claim correct? What is the correct evidence? $\newline$ Be sure to have all three parts of a CER answer: make a claim, provide evidence, and explain your reasoning for full credit.

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Q. Mary is making a decorative yard space with dimensions as shaded in green (

\triangle \mathrm{OAB})

\newline

Mary would like to cover the yard space with artificial turf (plastic grass-like rug).

\newline

Mary reasoned that she could draw a rectangle around the figure so that the point

O

was at a vertex of the rectangle and that points

A

and

B

were on sides of the rectangle. Then she reasoned that the three smaller triangles resulting could be subtracted from the area of the rectangle. Mary determined that she would need

28

square meters of artificial turf to cover the green shaded yard space pictured exactly.

\newline

Is Mary's reasoning and claim correct? What is the correct evidence?

\newline

Be sure to have all three parts of a CER answer: make a claim, provide evidence, and explain your reasoning for full credit.

Claim: Claim: Mary's reasoning and claim are incorrect.
Evidence: Evidence: To verify Mary's claim, we need to calculate the area of the rectangle and subtract the areas of the three smaller triangles.
Calculate Area: Let's assume the rectangle dimensions are $L$ (length) and $W$ (width). The area of the rectangle is $A_{\text{rect}} = L \times W$ .
Triangle Areas: The area of a triangle is $A_{\text{tri}} = \frac{1}{2} \times \text{base} \times \text{height}$ . There are three triangles to subtract from the rectangle's area.
Measurement Needed: Without the specific measurements of the rectangle and the triangles, we cannot calculate the exact area that Mary needs to cover with artificial turf.
Verification: Mary's claim of $28$ square meters cannot be verified without the dimensions. Therefore, we cannot conclude that her reasoning and claim are correct.