68.3k views
2 votes
The florida reef is the only coral reef in north america. it streches along Marion county to the dry tortugas national part. the florida reef contains the oldest known coral colony, which is over 300 years old. an oean scientist was studying the part of the protected area that extends from the dry tourgas to key west. she drew the area on the coordinate gird, as shown. as shown on the grid each square represents 100 square miles. determine the area, in square miles that the ocean scientist is studying round to the nearest tenth if necessary.

User SergeyA
by
8.4k points

1 Answer

6 votes

The area of the ocean the scientist is studying in square miles is 1,312.5 square miles

The steps used to find the area are presented as follows;

Please find attached the possible drawing of the area the ocean scientist drew, created with MS Excel

The area represented by each square on the grid = 100 square miles

The area of the drawing by the ocean scientist can be found using the composite area of a rectangle and a trapezoid, as follows;

Area of the rectangle is; (-5 - (-8.5)) × (-1.6 - (-5)) = 11.9 square units

Height, h, of the trapezoid with the base represented by a vertical line segment from ND to R, perpendicular to ND is; (-8.5 - (-9)) = 0.5

Length of the parallel sides are; (-1.6 - (-5)) = 3.4, and (-3.5 - (-5)) = 1.5

Area of the trapezoid is; (3.4 + 1.5) × 0.5/2 = 1.225

Area of the figure is; 11.9 + 1.225 = 13.125 square units

Area of the original ocean the scientist is studying is therefore;

Area = 100 × 13.125 = 1,312.5 square miles

The complete question obtained from a similar question found through search, can be presented as follows;

The Florida Reef is the only coral reef in North America. It stretches along Marin County to the Dry Tortugas National Park. The Florida Reef contains the oldest known coral colony, which is over 300 years old. An ocean scientist was studying the part of the protected that extends from the Dry Tortugas to Key West. She drew the area on the coordinate grid, as shown (please see attached diagram of the possible drawing by the scientist created with MS Excel)

Each square represents 100 square miles


\begin{tabular} c \cline{1-2}Vertex & Coordinate \\ \cline{1-2}D &(-5, -5) \\\cline{1-2}H & (-5, -1.6) \\\cline{1-2}N & (-9, -5)\\\cline{1-2}R & (-8.5, -1.6)\\\cline{1-2}W &(-9, -3.5) \\\cline{1-2}\end{tabular}

Determine the area in square miles, of the area that the ocean scientist is studying. Enter the response using the keypad below

The florida reef is the only coral reef in north america. it streches along Marion-example-1
User Ranjan Sarma
by
7.3k points