In an isosceles trapezoid, the base lengths are 20cm and 30cm, and the acute angle is 45. Find the area of the trapezoid.

univerkov | August 3, 2021 | education

Let’s draw the heights between the sides and the smaller base. We get that an acute angle with a degree measure of 45 ° will be equal to another acute angle in a right-angled triangle. The triangle will have equal sides, since the angles at the base are equal.

Let’s find the values of the lateral sides of right-angled triangles through the base difference:
30 – 20 = 10 cm – the sum of two sides that exceed the smaller base and adjacent to the sides.

Hence one of them

10: 2 = 5 cm.

each value is equal to the height, since these are the sides.

h = 5 cm.

We substitute the known values into the formula for the area of a trapezoid:

S = (a + b) h / 2 = ((20 + 30) 5) / 2 = (50 * 5) / 2 = 25 * 5 = 125 cm2 – the area of the trapezoid.

Answer: 125 cm2.

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