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Find the area of the quadrilateral Site ABCD when AB=20m, BC=40m, CD=28m, AD=15m, and angle ABC = 90 degrees.

a) 900 sq. meters
b) 1000 sq. meters
c) 1100 sq. meters
d) 1200 sq. meters

1 Answer

5 votes

Final answer:

The area of rectangle ABCD can be calculated as 800 sq. meters. However, since we don't have enough information about the triangle formed by AD, CD, and the perpendicular from D to AB, we cannot determine the total area of the quadrilateral SITE ABCD.

Step-by-step explanation:

To find the area of the quadrilateral SITE ABCD, we can divide it into two shapes: a rectangle (ABCD, with AB and CD as lengths and BC as width due to angle ABC being 90 degrees) and a triangle. Since AB = 20m and BC = 40m, the area of the rectangle ABCD is simply length × width, which is 20m × 40m = 800 sq. meters. However, we do not have enough information to calculate the area of the triangle formed by AD, CD, and the height from D to AB. Without the height or an angle, we cannot use the area formula for triangles nor Heron's formula. Therefore, with the given information, we cannot accurately calculate the total area of the quadrilateral.

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