Answer:
The height of trapezium is 6.01cm
Step-by-step explanation:
Given that the formula of area of trapezium is A = 1/2×(a+b)×h where a and b represents the length and h is the height. Next, you have to substitute the following values into the formula :
[tex]area = \frac{1}{2} \times (a + b) \times h[/tex]
[tex]let \: area = 42.7 \\ let \: a = 9.2 \\ let \: b = 5[/tex]
[tex]42.7 = \frac{1}{2} \times (9.2 + 5) \times h[/tex]
[tex]42.7 = \frac{1}{2} \times 14.2 \times h[/tex]
[tex]42.7 = 7.1 \times h[/tex]
[tex]h = 42.7 \div 7.1[/tex]
[tex]h = 6.01cm \: (3s.f)[/tex]
Test :
Let a = 9.2,
Let b = 5,
Let h = 6.01,
[tex]area = \frac{1}{2} \times (9.1 + 5) \times 6.01[/tex]
[tex]area = \frac{1}{2} \times 85.342[/tex]
[tex]area = 42.7 {cm}^{2} \: (proven)[/tex]
