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

Area = 1/2 * (sum of parallel sides) * height

However, we don't have the height. But we know that the non-parallel sides are each equal to 13 cm. This forms two right-angled triangles on either side of the trapezium.

We can find the height by using the Pythagorean theorem in one of the right-angled triangles. Let's take the triangle with the sides 13 cm (hypotenuse), 10 cm (base), and h (height).

According to the Pythagorean theorem, (hypotenuse)^2 = (base)^2 + (height)^2

So, (13)^2 = (10)^2 + h^2

= h^2 = (13)^2 - (10)^2

= h^2 = 169 - 100

= h^2 = 69

= h = sqrt(69)

Now, we can substitute the values into the area formula:

Area = 1/2 * (10 + 20) * sqrt(69)

= Area = 15 * sqrt(69) cm^2

So, the area of the trapezium is 15 * sqrt(69) cm^2.

Question

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

Area = 1/2 * (sum of parallel sides) * height

However, we don't have the height. But we know that the non-parallel sides are each equal to 13 cm. This forms two right-angled triangles on either side of the trapezium.

We can find the height by using the Pythagorean theorem in one of the right-angled triangles. Let's take the triangle with the sides 13 cm (hypotenuse), 10 cm (base), and h (height).

According to the Pythagorean theorem, (hypotenuse)^2 = (base)^2 + (height)^2

So, (13)^2 = (10)^2 + h^2

=> h^2 = (13)^2 - (10)^2

=> h^2 = 169 - 100

=> h^2 = 69

=> h = sqrt(69)

Now, we can substitute the values into the area formula:

Area = 1/2 * (10 + 20) * sqrt(69)

=> Area = 15 * sqrt(69) cm^2

So, the area of the trapezium is 15 * sqrt(69) cm^2.

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