Area of a Trapezium | Mensuration | Assessment | English | Grade 8

If the height of a trapezium is h and length of its parallel sides is a and b respectively, then the area of trapezium is _________.

• ½ × h × (a × b)

• ½ × h × (a - b)

• ½ × h × (a + b)

• ½ × h × (a/b)

Tags

CCSS.6.G.A.1

Area of the adjoining trapezium is _____.

• 272 cm²

• 285 cm²

• 80 cm²

• 2112 cm²

Answer explanation

Area of trapezium = ½ × h × (a + b) = ½ × 16 × (12 + 22 ) = 272 cm² So, Option 1 is correct.

Tags

CCSS.6.G.A.1

If the area of a trapezium is 462 cm² and the sum of its parallel sides is 42 cm, what is the height of the trapezium?

• 24 cm

• 22 cm

• 25 cm

• 20 cm

Answer explanation

Area of a trapezium = ½ × h ×(a + b) According to the question, we have, ½ × h × 42 cm = 462 cm² h = 462 cm²/ 42 cm i.e., h = 22 cm So, Option 2 is correct.

Tags

CCSS.6.G.A.1

The perimeter of a trapezium is 156 cm and its each non-parallel side is equal to 30 cm with its height 24 cm. Its area is ________.

• 1116 cm²

• 1062 cm²

• 1152 cm²

• 1008 cm²

Answer explanation

Perimeter of a trapezium = Sum of all its 4 sides According to the question, we have, 156 cm = 30 cm + 30 cm + sum of parallel sides (It is given that length of each non- parallel side = 30 cm) i.e. Sum of parallel sides = 156 - 60 = 96 cm Height of trapezium = 24 cm Area of trapezium = ½ × h × Sum of parallel sides = ½ × 96 cm × 24 cm = 1152 cm² So, option 3 is correct.

Tags

CCSS.6.G.A.1

Suraj wants to tile the floor of his trapezium shaped room as shown in figure. If the cost of tiles per sq. m is ₹ 120, what will be the total cost of the tiles?

• ₹ 218800

• ₹ 219400

• ₹ 217400

• ₹ 218400

Answer explanation

Area of trapezium = (1/2) × h ×(a + b) = (1/2) × 35 ×(48 + 56) = 1820 sq. m Cost of tiles per sq. m is ₹ 120 So, total cost of tiles = 1820 × 120 = ₹ 218400 Hence, Option 4 is correct.

Tags

CCSS.6.G.A.1

The area of a trapezium with equal non-parallel sides is 256 m². If the lengths of the parallel sides are 26 m and 38 m, find the length of the non-parallel sides.

• 12 m

• 10 m

• 16 m

• 15 m

Answer explanation

Area of trapezium = (1/2) × (Sum of parallel sides) × h According to the question, we have, 256 = (1/2) × (26 + 38) × h 256 = (1/2) × (64) × h 256 = 32 × h h = 256/32 i.e., h = 8 m Then, in the trapezium we can see that the length of non parallel side can be found by Pythagoras theorem AD² = DP² + AP² = 6² + 8² = 36 + 64 = 100 i.e., AD = 10 m As both unparallel sides are equal, so AD = BC = 10 m Hence, option 2 is correct.

Tags

CCSS.6.G.A.1