A trapezium has parallel sides of lengths 17 cm and 29 cm, and... | Mathematics MCQ | Examoogle

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A trapezium has parallel sides of lengths 17 cm and 29 cm, and the distance between them is 15 cm. What is the area of the trapezium?

335 cm $2$

315 cm $2$

325 cm $2$

345 cm $2$

Correct Answer

📐 MA • Math Direct FormulaMathematicsMensuration

Option D

345 cm $2$

Quick Summary:

Use the average of the two parallel sides: $\text{Average} = \frac{17 + 29}{2} = 23$ . Multiply this average by the distance: $23 \times 15 = 345$ .

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📐MAMath SolutionDirect Formula

📋 Given

Parallel sides (a) = 17 cm, (b) = 29 cm and distance (height) between them (h) = 15 cm.

🔢 Formula Used

Area=12×(a+b)×h\text{Area} = \frac{1}{2} \times (a + b) \times hArea=21​×(a+b)×h

⚡ Exam Hall Shortcut / Speed Trick

Use the average of the two parallel sides: $\text{Average} = \frac{17 + 29}{2} = 23$ . Multiply this average by the distance: $23 \times 15 = 345$ .

⚠️ Common Student Trap / Pitfall

Students often accidentally add the distance into the sum of the parallel sides or forget to divide by 2, leading to incorrect calculations.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Identify given values

Identify the length of parallel sides as $a = 17$ cm and $b = 29$ cm, and the height as $h = 15$ cm.

a=17,b=29,h=15a = 17, b = 29, h = 15a=17,b=29,h=15

Apply Area formula

Substitute the values into the standard area formula for a trapezium.

Area=12×(17+29)×15\text{Area} = \frac{1}{2} \times (17 + 29) \times 15Area=21​×(17+29)×15

Simplify and Calculate

Calculate the sum inside the parentheses: $17 + 29 = 46$ . Then multiply by half of 46 (which is 23) and the height (15).

Area=12×46×15=23×15=345\text{Area} = \frac{1}{2} \times 46 \times 15 = 23 \times 15 = 345Area=21​×46×15=23×15=345

✅

D is correct because the calculated area using the trapezium formula is 345 cm2.

Core Concepts Used

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Geometry Trapezium Area Mensuration

💡 EXAM TIP

This formula is a specific case of the area of a polygon; remember that any shape with parallel bases follows the logic of Average Width $\times$ Height.

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