ABCD is a right-angled trapezoid with area 8. The area of triangle ADB is 5. Then the area of triangle ABC is?
| July 2, 2021 | education
The area of the trapezoid is determined by the formula:
Savsd = (BC + AD) * AB / 2 = 8 cm2.
(BC + AD) * AB = 16 cm2.
BC * AB + AD * AB = 16 cm2. (1).
The area of the triangle ABD is equal to:
Savd = AB * AD / 2 = 5 cm2.
AB * AD = 10 cm2.
Let’s substitute in the first equation.
BC * AB + 10 = 16 cm2.
BC * AB = 6 cm2.
The area of the triangle ABC will be equal to:
Savs = BC * AB / 2 = 6/2 = 3 cm2.
Answer: The area of the triangle ABC is 3 cm2.
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