Question

Find the mean and round to the nearest tenth.

Answer 1

Area of second figure is 56.6 square meter

Solution:

Given that,

Two given figures are similar

Perimeter of first figure = 20 m

Perimeter of second figure = 34 m

Area of first figure = 19.6 square meter

Area of second figure = ?

Find the ratio of perimeter of first figure to second

$\frac{\text{perimeter of first figure}}{\text{perimeter of second figure}} = \frac{20}{34} = \frac{10}{17}$

In two similar triangles: The perimeters of the two triangles are in the same ratio as the sides

Therefore,

$\frac{\text{perimeter of first figure}}{\text{perimeter of second figure}} = \frac{10}{17}$

If two figures are similar, then ratio of their perimeters is equal to ratio of their sides

$\frac{\text{side of first figure}}{\text{side of second figure}} = \frac{10}{17}$

Taking square on both sides, then it becomes ratio of their areas

Because,

$area = side^2$

Therefore,

$(\frac{\text{side of first figure}}{\text{side of second figure}})^2 = (\frac{10}{17})^2\\\\\frac{\text{area of first figure}}{\text{area of second figure}} = (\frac{10}{17})^2\\\\\frac{19.6}{\text{area of second figure}} = \frac{100}{289}\\\\\text{area of second figure } = 19.6 \times \frac{289}{100}\\\\\text{area of second figure } = 56.644 \approx 56.6$

Thus area of second figure is 56.6 square meter