In a rectangular trapezoid, the sides are 7 cm and 25 cm, and the smaller base is 2 cm, find the area of the trapezoid.
January 2, 2021 | education
| Suppose given a rectangular trapezoid ABCD, in which:
angle A = 90 °,
lateral sides – AB = 7 cm, CD = 25 cm,
smaller base – BC = 2 cm.
Let us drop the perpendicular CO from the vertex of the trapezoid C to the side AD.
The area of the trapezoid ABCD will be defined as the sum of the areas of rectangle ABCO and right triangle CDO.
We calculate the area of the rectangle ABCO:
Spr = AB * BC = 7 * 2 = 14 cm ^ 2.
The area of the triangle CDO is:
Str = 1/2 * CO * OD.
CO = AB = 7 cm (as opposite sides of the rectangle ABCO).
Find OD:
OD ^ 2 = CD ^ 2 – CO ^ 2 = 25 ^ 2 – 7 ^ 2 = 625 – 49 = 576;
OD = √576 = 24 cm.
Then
Str = 1/2 * 7 * 24 = 84 cm ^ 2.
Find the area of the trapezoid ABCD:
S = Spr + Spr = 14 + 84 = 98 cm ^ 2.
Answer: 98 cm ^ 2.
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