Question 12 of 42intermediate🔧 ApplyNumerical3 marks

The parallel sides of a trapezium are 40 cm and 20 cm. If its non-parallel sides are both equal, each being 26 cm, find the area of the trapezium.

Correct Answer

720 cm2cm^{2}

Exercise: Exercise Set 6.2 | Q: 2 | (Page 25)
For More Understanding

Explanation

The area of a trapezium is calculated using the formula 1/2(a + b)h. To find the height, we divide the trapezium into a rectangle and two congruent right-angled triangles by dropping perpendiculars from the shorter base to the longer base. The base of each triangle is half the difference of the parallel sides, which allows us to use the Pythagorean theorem to find the height.

Solution Steps

  1. Step 1: Identify given values: parallel sides a = 40 cm and b = 20 cm, and equal non-parallel sides = 26 cm each.

  2. Step 2: Find the base of the right-angled triangles formed by dropping perpendiculars: (40 - 20) / 2 = 10 cm.

  3. Step 3: Use the Pythagoras theorem to find the height (h): h2h^{2} + 10210^{2} = 26226^{2} => h2h^{2} = 676 - 100 = 576 => h = 24 cm.

  4. Step 4: Calculate the area using the formula 1/2(a + b)h: 1/2(40 + 20) × 24 = 30×2430 \times 24 = 720 cm2cm^{2}.

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