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If the height of the trapezoid is 12 and the length of the two diagonals is 15 and 20 respectively, what is the area of the trapezoid? The answer should be 150 and 42. What about 42
The height of trapezoid is 12, and the length of two diagonals is 15 and 20 respectively,
Look at the picture
If the height of the trapezoid is 12 and the length of the two diagonals is 15 and 20 respectively, the area of the trapezoid is______ ．
In BDF of right triangle, BF = 152-122 = 9 can be obtained by Pythagorean theorem. In ace of right triangle, CE = 202-122 = 16, CE + BF = 25 = BC + EF ∵ EF = ad ∵ BC + ad = 25 ∵ trapezoid area = 25 × 12 △ 2 = 150 can be obtained by Pythagorean theorem. ② in BDF of right triangle, AE, DF and F of high trapezoid are on the extension line of BC, as shown in Figure 2 In ace, CE = ac2-ae2 = 152-122 = 9, AD + BC = BC + EF = BF + EC = 25, area of trapezoid = 12 (AD + BC) × AE = 12 (bf-ec) × AE = 12 × 25 × 12 = 150 can be obtained by Pythagorean theorem
If the height of the trapezoid is 12 and the length of the two diagonals is 15 and 20 respectively, the area of the trapezoid is 12______
One of them is 150 and the other is 42. I just don't know about 42
The area of a trapezoid is equal to the area of a triangle whose height is 12 on a bottom edge and whose diagonal length is 15 and 20 respectively. It can be proved by extending the length from the bottom to (top + bottom)
Thus, the length of bottom edge = (15 * 15-12 * 12) ^ (1 / 2) + (20 * 20-12 * 12) ^ (1 / 2) = 9 + 16 = 25
Triangle area = 12 * 25 / 2 = 150
So the area of the trapezoid is 150
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