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find the area of the trapezium in terms of x

Find The Area Of The Trapezium In Terms Of X class=

Sagot :

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Answer:

To find the area of trapezium \(ABCD\), we can use the formula for the area of a trapezium:

\[ \text{Area} = \frac{1}{2} (a + b) h \]

where \(a\) and \(b\) are the lengths of the two parallel sides (the bases), and \(h\) is the height of the trapezium.

In the trapezium \(ABCD\), we have the following:

- Top base \(AB = 13 \text{ cm}\)

- Bottom base \(DC = 17x + 12 \text{ cm}\)

- Height \(h = 5 \text{ cm}\)

So, the area of the trapezium is:

\[ \text{Area} = \frac{1}{2} (13 + (17x + 12)) \times 5 \]

Simplify the expression inside the parentheses:

\[ 13 + 17x + 12 = 17x + 25 \]

Now, substitute back into the area formula:

\[ \text{Area} = \frac{1}{2} (17x + 25) \times 5 \]

Multiply:

\[ \text{Area} = \frac{1}{2} \times 5 \times (17x + 25) \]

\[ \text{Area} = \frac{5}{2} (17x + 25) \]

So, the area of the trapezium in terms of \(x\) is:

\[ \text{Area} = \frac{85x + 125}{2} \]

\[ \text{Area} = 42.5x + 62.5 \text{ cm}^2 \]

Thus, the simplified area of the trapezium \(ABCD\) in terms of \

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