Answer :
Perimeter = sum of all the sides
let x = one side
longer side = x + 10
Perimeter = x + x + x + x + 10
62 = 4x + 10
4x = 52
x = 13
Longer side = 23
Area = (10+23)x2/10
= 6.6
let x = one side
longer side = x + 10
Perimeter = x + x + x + x + 10
62 = 4x + 10
4x = 52
x = 13
Longer side = 23
Area = (10+23)x2/10
= 6.6
The area of trapezoid is [tex]\boxed{216{\text{ c}}{{\text{m}}^2}}.[/tex]
Further explanation:
The formula of area of trapezoid can be expressed as follows,
[tex]\boxed{{\text{Area of trapezoid}} = \frac{1}{2} \times \left( {{\text{sum of parallel sides}}} \right) \times {\text{height}}}[/tex]
Given:
The perimeter of an isosceles trapezoid is 62 cm.
The length of the fourth side is [tex]10{\text{ cm}}.[/tex]
Explanation:
Consider the length of the side of trapezoid as [tex]x.[/tex]
Consider the longer side of the trapezoid as [tex]x+10.[/tex]
Perimeter of trapezoid is 62 cm.
[tex]\begin{aligned}{\text{Perimeter}}&= 62{\text{ cm}}\\x + x + x + x + 10 &= 62\\4x + 10 &= 62\\4x &= 62 - 10\\4x&= 52\\x&= \frac{{52}}{4}\\x&= 13\\\end{aligned}[/tex]
The longer side of the trapezoid is [tex]23{\text{ cm}}.[/tex]
The semi perimeter of triangle ABE can be obtained as follows,
[tex]\begin{aligned}S&= \frac{{a + b + c}}{2}\\&= \frac{{13 + 13 + 10}}{2}\\&= 18\\\end{aligned}[/tex]
The area of triangle ABE can be obtained as follows,
[tex]\begin{aligned}{\text{Area of }}\Delta ABE &= \sqrt {S \times \left( {S - a} \right) \times \left( {S - b} \right) \times \left( {S - c} \right)}\\&= \sqrt {18 \times \left( {18 - 13} \right)\left( {18 - 13} \right)\left( {18 - 10} \right)} \\&= \sqrt {18 \times 5 \times 5 \times 8}\\&= 5 \times12\\&= 60\\\end{aligned}[/tex]
The height of the trapezoid can be obtained as follows,
[tex]\begin{aligned}{\text{Area} &= 60\\\frac{1}{2}\times b\times h&= 60\\10 \timesh&= 120\\h&= 12\\\end{aligned}[/tex]
The height of the trapezoid is 12 cm.
The area of parallelogram ABED can be obtained as follows,
[tex]\begin{aligned}{\text{Area of ABED}}&= b\times h\\& = 13 \times12\\&= 156{\text{ c}}{{\text{m}}^2}\\\end{aligned}[/tex]
The area of trapezoid can be calculated as follows,
[tex]\begin{aligned}{\text{Area of ABCD}}&= {\text{Area of ABED}} + {\text{Area of BCE}} \\{\text{}}&=156 + 60\\&= 216{\text{ c}}{{\text{m}}^2}\\\end{aligned}[/tex]
The area of trapezoid is [tex]\boxed{216{\text{ c}}{{\text{m}}^2}}.[/tex]
Kindly refer to the image attached.
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Answer details:
Grade: Middle School
Subject: Mathematics
Chapter: Triangles
Keywords: triangle, triangle pair, equal angles, sides, area, trapezoid, two triangles, bases, intersecting, diagonal, segment, sector, minor segment.
