Calculate Trapezoid Area with Bases 9 and 12, Height 5 Units

Trapezoid Area with Given Base Lengths

Given the trapezoid:

999121212555AAABBBCCCDDDEEE

What is the area?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 What is the area of the trapezoid?
00:06 Let's substitute the side lengths according to the given data
00:12 We'll use the formula for calculating trapezoid area
00:15 (height(AE) multiplied by the sum of bases(AB+DC)) divided by 2
00:25 Let's substitute the appropriate values and solve for the area
00:38 Always solve parentheses first
00:55 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Given the trapezoid:

999121212555AAABBBCCCDDDEEE

What is the area?

2

Step-by-step solution

Formula for the area of a trapezoid:

(base+base)2×altura \frac{(base+base)}{2}\times altura

We substitute the data into the formula and solve:

9+122×5=212×5=1052=52.5 \frac{9+12}{2}\times5=\frac{21}{2}\times5=\frac{105}{2}=52.5

3

Final Answer

52.5

Key Points to Remember

Essential concepts to master this topic
  • Formula: Area = (b1+b2)2×h \frac{(b_1 + b_2)}{2} \times h where bases are parallel sides
  • Technique: Add bases first: 9 + 12 = 21, then divide by 2
  • Check: Final calculation: 212×5=52.5 \frac{21}{2} \times 5 = 52.5 square units ✓

Common Mistakes

Avoid these frequent errors
  • Using the wrong sides as bases
    Don't use adjacent sides like base and height as both bases = wrong area! The slanted sides are NOT bases. Always identify the two parallel sides (top and bottom) as your bases before applying the formula.

Practice Quiz

Test your knowledge with interactive questions

Calculate the area of the trapezoid.

555141414666

FAQ

Everything you need to know about this question

How do I identify which sides are the bases?

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The bases are always the two parallel sides of the trapezoid. In this problem, they're the top side (length 9) and bottom side (length 12). The slanted sides are just connecting lines, not bases!

Why do we divide the sum of bases by 2?

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Dividing by 2 gives us the average length of the two bases. Think of it as finding the length of a rectangle with the same area - it would have this average width!

What if I multiply the bases instead of adding them?

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Multiplying bases gives you a completely wrong area! The trapezoid formula specifically requires adding the bases first: (9 + 12) ÷ 2 × 5, not 9 × 12 × 5.

Can I use any side as the height?

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No! The height must be the perpendicular distance between the two parallel bases. It's shown as the vertical line (length 5) in the diagram, not the slanted sides.

Why is my answer 52.5 instead of a whole number?

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Decimal answers are perfectly normal in geometry! The calculation 1052=52.5 \frac{105}{2} = 52.5 is exact and correct. Always express your final area with appropriate units.

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