The fences of a wildlife park form a trapezium. The two parallel sides of trapezium are 18 km and 12 km long. The perpendicular distance between them is $$ 9,7 \mathrm{~km} $$. What is the area of the wildllife park in $$ \mathrm{km}^{2} $$ ?

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The area of the wildlife park is 145.5 km². To find the area of a trapezium (trapezoid), we can use the formula: $$ \text{Area} = \frac{1}{2} \times (b_1 + b_2) \times h $$ where $$ b_1 $$ and $$ b_2 $$ are the lengths of the two parallel sides, and $$ h $$ is the height (the perpendicular distance between the parallel sides). In this case: - $$ b_1 = 18 $$ km (the longer parallel side) - $$ b_2 = 12 $$ km (the shorter parallel side) - $$ h = 9.7 $$ km (the perpendicular distance between the parallel sides) Now, substituting these values into the formula: $$ \text{Area} = \frac{1}{2} \times (18 + 12) \times 9.7 $$ Calculating the sum of the parallel sides: $$ 18 + 12 = 30 $$ Now substituting this back into the area formula: $$ \text{Area} = \frac{1}{2} \times 30 \times 9.7 $$ Calculating $$ \frac{1}{2} \times 30 $$: $$ \frac{1}{2} \times 30 = 15 $$ Now, multiplying by the height: $$ \text{Area} = 15 \times 9.7 = 145.5 $$ Thus, the area of the wildlife park is $$ \boxed{145.5} \text{ km}^2. $$

The fences of a wildlife park form a trapezium. The two parallel sides of trapezium are 18 km and 12 km long. The perpendicular distance between them is \( 9,7 \mathrm{~km} \). What is the area of the wildllife park in \( \mathrm{km}^{2} \) ?

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The fences of a wildlife park form a trapezium. The two parallel sides of trapezium are 18 km and 12 km long. The perpendicular distance between them is \( 9,7 \mathrm{~km} \). What is the area of the wildllife park in \( \mathrm{km}^{2} \) ?

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