1. Find the area of the trapezium whose parallel sides are 22 cm and 31 cm respectively, and the distance between them is 12 cm.
2. The area of a trapezium is 320 sq.cm and distance between the parallel sides is 20 cm.if one of the parallel sides is 16 cm,find the length of another parallel side.
3. Find the area of a rhombus if:
a) Each side is 16 m and height is 9 m
b) Each diagonals are 20 cm and 18 cm.
4. The area of a rhombus is 256 sq.cm and one of the diagonals is 32 cm.find the length of other diagonal.
5. The area of a triangle with a base of 8 cm is 24 sq.cm.find its altitude from this base.
6. Find the lateral surface area,total surface area and volume of a cube of:
a) Side=70cm
b)side=25cm
Answers
1. Area of trap = sum of parallel sides × height
= 22+31 ×12
= 394
2. Again , Area = Sum of parallel sides × height
= > 320 = (16+x) × 20
320/20 = 16+x
16 - 16 = x
x = 1cm
3. (a) Area of rhombus = b × h
= 16×9
= 144
(b) Area = 1/2 d1 d2
= 1/2 × 20 × 18
= 180
4. 256= 1/2*32*x
x = 16
5. area = 1/2*b*h
24= 1/2*8*x
x=6cm
Hope it helps you buddy :)
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Knowledge required
→ar(trapezium) = 1/2×(sum of || sides)×(distance b/w || sides)
→ar(rhombus) = 1/2×(product of diagonals)
also
→ar (rhombus) = base×height
(because rhombus is also a parallelogram)
→ ar(triangle) = 1/2×base×altitude
→ LSA of cube = 4(side)²
→TSA of cube = 6(side)²
→Volume of cube = (side)³
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Solution 1
given parallel sides = 22 cm and 31 cm
distance b/w parallel sides = 12 cm
ar(trapezium) = 1/2×(22+31)×(12)
ar(trapezium) = 318 cm² (Ans.)
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Solution 2
area of trapezium = 320 cm²
distance b/w parallel sides = 20 cm
one of parallel side is = 16 cm
let, length of other parallel side = x
then,
320 = 1/2×(16+x)×(20)
320×2/20=16+x
32 = 16+x
x = 16 cm (Ans.)
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Solution 3
a) each side given = 16 m
height = 9 m
ar (rhombus) = 16 * 9
ar(rhombus) = 144 m² (Ans.)
b) diagonals are 20 cm and 18 cm each
ar(rhombus) = 1/2×(20×18)
ar(rhombus) = 180 cm² (Ans.)
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Solution 4
area of rhombus is = 256 cm²
one of diagonal is = 32 cm
let, length of other diagonal = x
then,
256 = 1/2×32× x
x = 256*2 / 32
x = 16 cm (Ans.)
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Solution 5
area of triangle = 24 cm²
base of triangle = 8 cm
let, altitude of triangle = h
then,
1/2×8×h = 24
h = 24*2/8
h = 6 cm (Ans.)
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Solution 6
a) side = 70 cm
LSA of cube= 4 (70)²= 19600 cm²
TSA of cube = 6 (70)² = 29400 cm²
volume of cube = (70)³ = 343000 cm³
b) side = 25 cm
LSA of cube = 4(25)² = 2500 cm²
TSA of cube = 6(25)² = 3750 cm²
Volume of cube = (25)³ = 15625 cm³
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