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3. The length of two parallel sides of a trapezium are 5 meter and 7 meter. If the distance between them is 8 meter. Find the area of the trapezium.

4. Area of a trapezium is 20 cm². Length of the parallel sides are 3 cm and 7 cm. Find the distance between the parallel sides.

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[tex]\huge{\underline{\boxed{{\pmb{\sf{ \: TRAPEZIUM \: }}}}}}[/tex]

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Answer #1: [tex]\boxed{\sf{48 \: m^2}}[/tex]

Answer #2: [tex]\boxed{\sf{4 \: cm}}[/tex]

SOLUTION:

#1.

» Given that,

The length of the first side,

  • a = 5 meter

Length of the second side,

  • b = 7 meter

Distance between the parallel sides,

  • d = 8 meter

» We know the area is:

  • [tex]\sf =\frac{1}{2} = sum \; of \; parallel [/tex]

  • [tex]\sf sides = distance \: between \: parallel \: sides[/tex]

  • [tex]\sf =\frac{1}{2} \times (a+b) \times d[/tex]

  • [tex]\sf =\frac{1}{2} \times (5 + 7) \times 8[/tex]

  • [tex]\sf =\frac{1}{2} \times 12 \times 8[/tex]

  • [tex]\sf = 48 \: m^2[/tex]

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#2.

» Given that,

The length of the first side,

  • a = 3 cm

The length of the second side,

  • b = 7 cm

Distance between the parallel sides,

  • d = 7

» Area A of the trapezium is:

  • [tex]\sf A = \frac{1}{2} \times (a + b) \times d[/tex]

  • [tex]\sf 20 = \frac{1}{2} \times (3 + 7) \times d[/tex]

  • [tex]\sf 20 = \frac{1}{2} \times 10 \times d[/tex]

  • [tex]\sf 5 \times d = 20[/tex]

  • [tex]\sf d = \frac{20}{5}[/tex]

  • [tex]\sf d = 4 \: cm[/tex]

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