Question

Consider two similar parallelograms with a matching sides in the ratio 4:6. Calculate the area of the larger parallelogram if the area of the smaller parallelogram is 32 cm².

A) 48 cm²
B) 64 cm²
C) 24 cm²
D) 36 cm²

Answer 1

The area of the larger parallelogram can be found by using the ratio of the sides of the parallelograms. The sides of the larger parallelogram are 4/6 times the length of the sides of the smaller parallelogram. The area of the larger parallelogram is 64 cm².

Step-by-step explanation:

The area of the larger parallelogram can be found by using the ratio of the sides of the parallelograms. The sides of the larger parallelogram are 4/6 times the length of the sides of the smaller parallelogram. Since the area of the smaller parallelogram is given as 32 cm², we can calculate the area of the larger parallelogram as follows:

Let x be the length of a side of the smaller parallelogram. Then the length of a side of the larger parallelogram is (4/6)x = (2/3)x.

The area of the larger parallelogram can be calculated by multiplying the lengths of its sides:

Area of larger parallelogram = length of side x length of side = (2/3)x x (2/3)x = (4/9)x².

Since we know that the area of the smaller parallelogram is 32 cm², we can set up the following equation:

32 = (4/9)x²

Solving this equation will give us the value of x, and we can then use it to calculate the area of the larger parallelogram.

Therefore, the correct answer is B) 64 cm².