Question

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What is the area of the irregular polygon shown below?
O
A. 65 sq. units
O
B. 49 sq. units
O
C. 105 sq. units
O
D. 35 sq. units

Answer 1

Option B: 49 square units.

Explanation:

The irregular polygon consists of a rhombus a square.

Area of rhombus = 0.5*(product of diagonals).

Area of square = length * length = l^2.

The diagonals of the rhombus measure 8 units and 6 units respectively. The diagram shows the length of half of the diagonals, so doubling both the lengths gives us the required lengths. The side of the square measures 5 units. Substituting all the information in the formula:

Total Area = Area of rhombus + Area of square.

Total Area = 0.5*8*6 + 5^2.

Total Area = 24 + 25

Total Area = 49 square units.

Therefore, Option B is the correct answer!!!