Question

for a parallelogram whose sides are 26 cm and 23 cm, which of the following is true? complete parts (a) through (d) below. a. the data are insufficient to enable us to determine the area. choose the correct answer below. a. the statement is false. the area of a parallelogram is equal to the product of its side lengths. b. the statement is false. the area of a parallelogram is equal to the sum of its side lengths. c. the statement is true. the height is unknown, but it is needed to determine the area. d. the statement is true. the exact shape is not known, which is needed to determine which formula for the area to use.

Explanation:

The area formula for a parallelogram is \(A = base\times height\). Here, only the side - lengths (which can be considered as base and adjacent side) are given. Without knowing the height corresponding to the base (or an angle to calculate the height using trigonometry if we assume some geometric relations), we cannot calculate the area.

• Option A: The area of a parallelogram is not \(A = a\times b\) (where \(a\) and \(b\) are side - lengths). The formula \(A = a\times b\) is for a rectangle (a special case of a parallelogram where the height is equal to the adjacent side).
• Option B: The sum of side - lengths (\(a + b+a + b\)) gives the perimeter, not the area.
• Option C: The formula for the area of a parallelogram \(A = b\times h\) (where \(b\) is the base and \(h\) is the height). Since we know the base (\(b = 26\) or \(b = 23\)), but the height \(h\) is unknown, we cannot calculate the area.
• Option D: The formula for the area of a parallelogram is always \(A = b\times h\). We do not need to know the "exact shape" in the sense of some non - standard formula. The problem is the lack of height information.

Answer:

C. The statement is true. The height is unknown, but it is needed to determine the area.