Question

the parallel sides a and b of the trapezium/trapezoid are: a = 6 cm, b = 10 cm and the vertical height between them, h is given by: h = 5 cm what is the area of this trapezium/trapezoid?

Explanation:

Step1: Recall the formula for the area of a trapezoid

The formula for the area \( A \) of a trapezoid is \( A=\frac{1}{2}(a + b)h \), where \( a \) and \( b \) are the lengths of the parallel sides, and \( h \) is the height between them.

Step2: Substitute the given values into the formula

We are given \( a = 6\space\text{cm} \), \( b = 10\space\text{cm} \), and \( h = 5\space\text{cm} \). Substituting these values into the formula, we get:

$$ A=\frac{1}{2}(6 + 10)\times5 $$

Step3: Simplify the expression

First, calculate the sum inside the parentheses: \( 6+10 = 16 \). Then, multiply this result by \( \frac{1}{2} \) and \( 5 \):

$$ A=\frac{1}{2}\times16\times5 $$

$$ A = 8\times5 $$

$$ A=40 $$

Answer:

The area of the trapezium/trapezoid is \( 40\space\text{cm}^2 \).