The diagonal of an isosceles trapezoid is perpendicular to the lateral side. The height drawn from the top of the obtuse angle divides the base into segments 20 and 5 in length. Find the area of the trapezoid.
1. The tops of the trapezoid – A, B, C, D. AH = 5 cm. DH = 20 cm. BH – height.
2. The length of the segment DH, according to the properties of an isosceles trapezium, is calculated by the formula:
DH = (AD + BC) / 2.
3. Using this formula, we calculate the length of the BC – the smaller base of the trapezoid:
(АD + ВС) / 2 = 20 cm ..
AD = 5 + 20 = 25 cm.
AD + BC = 40 cm ..
BC = 40 – 25 = 15 cm.
4. We calculate the length of the HV height:
BH = √AH x DH = √5 x 20 = √100 = 10 cm.
5. The area of the trapezoid is equal to (AD + BC) / 2 x BH = (25 + 15) / 2 x 10 = 200 cm².
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