A sandpit is designed in the shape of a trapezium, with the dimensions: 5m=height, base 1=(x+4)m, base 2=(x+10)m. If the area of the sandpit is 14 metres squared, determine its perimeter

The area \( A \) of a trapezium with height \( h \) and bases \( a \) and \( b \) is given by the formula:

\[
A = \frac{1}{2} \times (a + b) \times h
\]

Given:
- Height, \( h = 5 \) meters
- Base 1, \( a = x + 4 \) meters
- Base 2, \( b = x + 10 \) meters
- Area, \( A = 14 \) square meters

### Step 1: Set Up the Area Equation
Substitute the values into the area formula:

\[
14 = \frac{1}{2} \times ((x + 4) + (x + 10)) \times 5
\]

Simplify the expression inside the parentheses:

\[
14 = \frac{1}{2} \times (2x + 14) \times 5
\]

Now, distribute and simplify:

\[
14 = (x + 7) \times 5
\]
\[
14 = 5x + 35
\]

### Step 2: Solve for \( x \)
Rearrange to solve for \( x \):

\[
5x = 14 - 35
\]
\[
5x = -21
\]
\[
x = -\frac{21}{5} = -4.2
\]

### Step 3: Find the Lengths of the Bases and Height
Now, substitute \( x = -4.2 \) back into the expressions for the bases:
- Base 1: \( x + 4 = -4.2 + 4 = -0.2 \) meters (This would actually imply an error; bases should not be negative). Let's re-evaluate this

A sandpit is designed in the shape of a trapezium, with the dimensions: 5m=height, base 1=(x+4)m, base 2=(x+10)m. If the area of the sandpit is 14 metres squared, determine its perimeter.

Solve a geometry problem to find the perimeter of a trapezium-shaped sandpit. Given dimensions include height = 5m, bases as expressions in x, and area = 14m². Learn to set up and solve for x using the area formula for trapeziums, followed by perimeter calculation. Suitable for Grades 9-10.

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