Question

The pair of figures to the right are similar. The area of one figure is given. Find the area of the other figure to the nearest whole number.Area of smaller parallelogram5 ft30 ft larger parallelogram baseTwo similar figures: the first has side length 5 feet and the other of side length 30 feet.Question content area bottomPart 1The area of the larger parallelogram is.(Round to the nearest whole number as needed.)

Answer 1

We want to solve the question below

The formula for the relationship between the lengths and areas of two similar plane figure is given as

`\begin{gathered} (A_s)/(A_l)=((l_s)/(l_l))^2 \\ Where\text{ A}_s\text{ and l}_s\text{ are the area and length of one side of the small figure } \\ And\text{ } \\ A_l\text{ and l}_l\text{ are the area and length of one side of the large figure } \end{gathered}`

Plugging in the values from the question into the formula, we have

`\begin{gathered} (A_s)/(A_l)=((l_s)/(l_l))^2 \\ (25)/(A_l)=((5)/(35))^2 \\ (25)/(A_l)=(25)/(1225) \\ cross\text{ multiplying we have } \\ 25A_l=1225*25 \\ A_l=(1225*25)/(25) \\ =1225ft^2 \end{gathered}`

Hence the answer is 1225