Question

Дано: АД= 18 см, ВС= 2 см, АС=15 см, ВД=7 см. найти площадь трапеции

Answer 1

S=0,5(a+b)h;S= 0.5(2+18)2=20

Answer 2

Calculation of the Trapezoid's Area

To find the area of a trapezoid, we can use the formula:

Area = (sum of the lengths of the parallel sides) * (height) / 2

Given the following measurements: - AD = 18 cm - BC = 2 cm - AC = 15 cm - BD = 7 cm

We need to find the area of the trapezoid.

Solution:

To find the height of the trapezoid, we can use the Pythagorean theorem. The height is the perpendicular distance between the parallel sides.

Let's label the points as follows: - A: The top left corner of the trapezoid - B: The top right corner of the trapezoid - C: The bottom right corner of the trapezoid - D: The bottom left corner of the trapezoid

We have the following measurements: - AD = 18 cm - BC = 2 cm - AC = 15 cm - BD = 7 cm

Using the Pythagorean theorem, we can find the height (h) of the trapezoid:

h^2 = AC^2 - (AD - BC)^2

Substituting the given values, we have:

h^2 = 15^2 - (18 - 2)^2

Simplifying the equation:

h^2 = 225 - 16

h^2 = 209

Taking the square root of both sides:

h = sqrt(209)

Now that we have the height, we can calculate the area of the trapezoid using the formula:

Area = (AD + BC) * h / 2

Substituting the given values, we have:

Area = (18 + 2) * sqrt(209) / 2

Simplifying the equation:

Area = 20 * sqrt(209) / 2

Area = 10 * sqrt(209)

Therefore, the area of the trapezoid is 10 * sqrt(209) square cm.

Let me know if there's anything else I can help you with!