Identify trapeziums :
What is trapezium ?
A quadrilateral in which one pair of opposite sides is parallel called trapezium.
Various types of trapeziums are,
Right trapezoid :
A right trapezoid (also called right-angled trapezoid) has two adjacent right angles. Right trapezoids are used in the trapezoidal rule for estimating areas under a curve.
Acute trapezoid :
An acute trapezoid has two adjacent acute angles on its longer base edge
Obtuse trapezoid :
An obtuse trapezoid has one acute and one obtuse angle on each base.
Isosceles trapezoid :
An isosceles trapezoid is a trapezoid where the sides (legs) have the same length, and the base angles have the same measure. It has reflection symmetry. This is possible for acute or right trapezoids.
A parallelogram is a trapezoid with two pairs of parallel sides. A parallelogram has central 2-fold rotational symmetry (or point reflection symmetry). It is possible for obtuse or right trapezoids.
A tangential trapezoid is a trapezoid that has an incircle.
Area = (1/2) (a + b) x h
Example 1 :
In a trapezium the measurement of one parallel side two more than the other parallel side and the height is 4 cm. The area of the trapezium is 64 cm². Find the two parallel sides.
Area of the trapezium = 64 cm²
Let "a" and "b" are two parallel sides
One parallel side is two more than the other parallel side. So we can assume b as a + 2
Area of a trapezium = (1/2) (a + b) x h
(1/2) (a + b) x h = 64
(1/2) (a + a + 2) x 4 = 64
(1/2) (2a + 2) x 4 = 64
2 (2a + 2) = 64 ==> 2a + 2 = 32
2a = 30 ==> a = 15 cm
b = a + 2 ==> b = 15 + 2 ==> b = 17 cm
Therefore the two parallel sides are 15 cm and 17 cm.
Example 2 :
The height of a trapezoid is 8 in. and its area is 96 square inches. One base of the trapezoid is 6 inches longer than the other base. What are the lengths of the bases?
here, h = 8 inches
Area of the trapezoid = 96 square inches
base lengths are b₁ and b₂ respectively.
b₁ = b₂ + 6
(1/2) x 8 (b₂ + 6 + b₂) = 96
4 (2b₂ + 6) = 96
2b₂ + 6 = 24
2b₂ = 18
b₂ = 9
By applying the value of b₂ in the equation b₁ = b₂ + 6, we get
b₁ = 9 + 6 ==> b₁ = 15 inches
Hence, base lengths are 9 inches and 15 inches
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