问题1.找到梯形的面积(以平方米为单位)，梯形的基本面和高度如下：
(i)基准= 12 dm和20 dm，海拔= 10 dm
(ii)底座= 28厘米和3 dm，高度= 25厘米
(iii)基地= 8 m和60 dm，海拔= 40 dm
(iv)底座= 150厘米和30 dm，高度= 9 dm
解决方案：
Area of trapezium = 1/2 (Sum of lengths of parallel sides) × altitude
(i) Given:
Length of bases of trapezium = 12 dm and 20 dm,
Length of altitude = 10 dm
As we know that 10 dm = 1 m
Therefore, Length of bases in m is 1.2 m and 2 m.
Similarly, length of altitude in m is 1 m.
Now, put the values in the formula(i.e. Area of trapezium),
Area of trapezium = 1/2 (1.2 + 2.0) × 1 = 1/2 × 3.2 = 1.6
Hence, Area of trapezium = 1.6m2
(ii) Given:
Length of bases of trapezium = 28 cm and 3 dm,
Length of altitude = 25 cm,
As we know that 10 dm = 1 m
Therefore, Length of bases in m = 0.28 m and 0.3 m
and length of altitude in m = 0.25 m
Now, put the values in the given formula(i.e. Area of trapezium),
Area of trapezium = 1/2 (0.28 + 0.3) × 0.25 = 1/2 × 0.58× 0.25 = 0.0725
Hence, Area of trapezium = 0.0725m2
(iii) Given:
Length of bases of trapezium = 8 m and 60 dm,
Length of altitude = 40 dm.
As we know that 10 dm = 1 m
Therefore, Length of bases in m = 8 m and 6 m
and length of altitude in m = 4 m
Now, put the values in the given formula(i.e. Area of trapezium),
Area of trapezium = 1/2 (8 + 6) × 4 = 1/2 × 56 = 28
Hence, Area of trapezium = 28m2
(iv) Given:
Length of bases of trapezium = 150 cm and 30 dm,
Length of altitude = 9 dm.
As we know that 10 dm = 1 m
Therefore, Length of bases in m = 1.5 m and 3 m
and length of altitude in m = 0.9 m.
Now, put the values in the given formula(i.e. Area of trapezium),
Area of trapezium = 1/2 (1.5 + 3) × 0.9 = 1/2 × 4.5 × 0.9 = 2.025
Hence, Area of trapezium = 2.025m2
问题2.如果平行于给定底部的边长为9 cm，则找到底部为15 cm，高度为8 cm的梯形区域。
解决方案：
Given:
Length of bases of trapezium = 15 cm and 9 cm,
Length of altitude = 8 cm.
As we know that,
Area of trapezium = 1/2 (Sum of lengths of parallel sides) × altitude
Now, put all the given values in this formula, and we get,
Area of trapezium = 1/2 (15 + 9) × 8 = 1/2 × 192 = 96
Hence, the area of trapezium = 96m2
问题3.找到梯形的面积，梯形的平行边的长度分别为16 dm和22 dm，高度为12 dm。
解决方案：
Given:
Length of bases of trapezium = 16 dm and 22 dm,
Length of altitude = 12 dm.
As we know that 10 dm = 1 m
Therefore, the length of bases in m = 1.6 m and 2.2 m
and length of altitude in m = 1.2 m.
As we know that,
Area of trapezium = 1/2 (Sum of lengths of parallel sides) × altitude
Now, put all the given values in this formula, and we get,
Area of trapezium = 1/2 (1.6 + 2.2) × 1.2 = 1/2 × 3.8 × 1.2 = 2.28
Hence, the Area of trapezium = 2.28m2
问题4.求出梯形的高度，梯形的底长(平行边)为60 cm，面积为600 cm 2 。
解决方案：
Given:
Length of bases of trapezium = 60 cm,
Area = 600 cm2
As we know that,
Area of trapezium = 1/2 (Sum of lengths of parallel sides) × altitude
Now, put all the given values in this formula, and we get,
600 = 1/2 (60) × altitude
600 = 30 × altitude
altitude = 600/30 = 20
Hence, the length of altitude is 20 cm.
问题5.找出一个梯形的高度，该梯形的面积为65 cm 2 ，其底面为13 cm和26 cm。
解决方案：
Given:
Length of bases of trapezium = 13 cm and 26 cm,
Area = 65 cm2
As we know that,
Area of trapezium = 1/2 (Sum of lengths of parallel sides) × altitude
Now, put all the given values in this formula, and we get,
65 = 1/2 (13 + 26) × altitude
65 = 39/2 × altitude
altitude = (65×2) /39 = 130/39 = 10/3
Hence, the length of altitude = 10/3 cm
问题6.计算面积为4.2 m 2且高度为280 cm的梯形的底长总和。
解决方案：
Given:
Height of trapezium = 280 cm = 2.8m,
Area = 4.2 m2,
As we know that,
Area of trapezium = 1/2 (Sum of lengths of parallel sides) × altitude
We can also rewrite the formula as,
Sum of lengths of parallel sides = (2 × Area) / altitude
= (2 × 4.2) / 2.8 = 8.4/2.8 = 3
Hence, the sum of lengths of parallel sides = 3 m
问题7.找到梯形的面积，梯形的平行边长分别为10厘米和15厘米，彼此之间的距离为6厘米。计算该面积为
(i)两个三角形和一个矩形的面积之和。
(ii)矩形的面积与两个三角形的面积之和之差。
解决方案：
(i) As we know that,
Area of a trapezium ABCD = area of ∆DFA + area of rectangle(DFEC) + area of ∆CEB
= (1/2 × AF × DF) + (FE × DF) + (1/2 × EB × CE)
= (1/2 × AF × h) + (FE × h) + (1/2 × EB × h)
= 1/2 × h × (AF + 2FE + EB) = 1/2 × h × (AF + FE + EB + FE)
= 1/2 × h × (AB + FE)
= 1/2 × h × (AB + CD) -(Opposite sides of rectangle are equal)
= 1/2 × 6 × (15 + 10) = 1/2 × 6 × 25 = 75
Hence, the area of trapezium = 75 cm2
(ii) Area of rectangle ABEF = 15 x 6 = 90 cm2
Area of ∆ADF + ∆BEC = 1/2 (FD + CE) x DM
= 1/2 x (15 – 10) x 6 = 1/2 x 5 x 6 = 15 cm2
Area of trapezium = 90 – 15 = 75 cm² -(Area of rectangle – Area of two triangles)
Hence the difference of the area of a rectangle and
the sum of the areas of two triangles is 75 cm2
问题8.梯形的面积为960 cm 2 。如果平行边分别为34 cm和46 cm，请找到它们之间的距离。
解决方案：
As we know that,
Area of trapezium = 1/2 (Sum of lengths of parallel sides) × distance between parallel sides(height)
Also, we can rewrite the formula as,
Distance between parallel sides = (2 × Area) / Sum of sides
Now, put all the given values in this formula, and we get,
= (2 × 960) / (34 + 46) = (2 × 960) / 80 = 1920/80 = 24
Hence, the distance between parallel sides = 24 cm
问题9.找到图的面积作为两个梯形和一个矩形的面积之和。
解决方案：
Given:
Length of rectangle = 50 cm
Breadth of rectangle = 10 cm
Length of the parallel sides of the trapezium = 30 cm and 10 cm
Distance between parallel sides of trapezium = (70 – 50)/2 = 20/2 = 10
So, the height of the trapezium is 10cm
From the given figure we conclude that,
Area of figure = Area of two trapeziums + Area of rectangle
= 2 × 1/2 (Sum of lengths of parallel sides) × altitude + Length × Breadth
Now, put all the given values in this formula, and we get,
= 2 × 1/2 (30+10) × 10 + 50 × 10 = 40 × 10 + 50 × 10
= 400 + 500 = 900
Hence, the area of figure = 900 cm2
问题10.桌子的顶部形状为梯形。如果其平行边分别是1 m和1.2 m，并且它们之间的垂直距离是0.8 m，请找到其面积。
解决方案：
Given:
Length of the parallel sides of the trapezium = 1.2m and 1m,
Distance between parallel sides of trapezium(height) = 0.8m
As we know that,
Area of trapezium = 1/2 (Sum of lengths of parallel sides) × distance between parallel sides
Now, put all the given values in this formula, and we get,
Area of trapezium = 1/2 (1.2 + 1) × 0.8 = 1/2 × 2.2 × 0.8 = 0.88
Hence, the area of trapezium = 0.88m2