MNKP-trapezoid. NK and MP-bases of the trapezoid, NK: MP = 2: 6. The area of the trapezoid is 96.
| April 27, 2021 | education
MNKP-trapezoid. NK and MP-bases of the trapezoid, NK: MP = 2: 6. The area of the trapezoid is 96. Find the area of the triangle MNK.
Let NK = 2a, then MP = 6a; h – height NB;
The area of the trapezoid is (2a + 6a) * h / 2 = 4a * h; 4a * h = 96; a * h = 24;
The area of a triangle NPM is 6a * h / 2 = 3a * h = 3 * 24 = 72;
The area of the triangle MNK is 96 – 72 = 24;
Answer: The area of the triangle MNK is 24.
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