In the AKDE trapezoid with the base AE = 15m and KD = 9dm, a DC segment is drawn parallel to the side of the AK.

| July 22, 2021 | education

In the AKDE trapezoid with the base AE = 15m and KD = 9dm, a DC segment is drawn parallel to the side of the AK. The area of the triangle CDE = 36 dm. Find the area of the trapezoid.

Given:
trapezium AKDE,
AE – 15 dm,
DC section parallel to the AK side,
S CDE = 36 dm.
Find the area of a trapezoid AKDE -?
Decision:
1) Consider the trapezoid AKDE. Since DC is parallel to the side of AK, then KD = AC = 9 dm, CE = AE – CE, CE = 15 – 9 = 6 dm;
2) Let’s draw the height of the CH. Consider the triangle CDE. The area of the triangle CDE is found by the formula:
S CDE = 1/2 * DH * CE;
S CDE = 1/2 * DH * 6;
36 = 3 * DH;
DH = 36: 3;
DH = 12 dm;
3) S AKDE = (KD + AE) / 2 * DH;
S AKDE = (9 + 15) / 2 * 12;
S AKDE = 24/2 * 12;
S AKDE = 12 * 12;
S AKDE = 144 decimetres squared.
Answer: 144 decimetres squared.



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