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mrs_skeptik [129]
2 years ago
13

the perimeter of an isosceles trapezoid is 62 cm. if three sides are equal in length and the fourth side is 10 cm longer, find t

he area of the trapezoid.

Mathematics
2 answers:
Alja [10]2 years ago
5 0
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  
brilliants [131]2 years ago
3 0

The area of trapezoid is \boxed{216{\text{ c}}{{\text{m}}^2}}.

Further explanation:

The formula of area of trapezoid can be expressed as follows,

\boxed{{\text{Area of trapezoid}} = \frac{1}{2} \times \left( {{\text{sum of parallel sides}}} \right) \times {\text{height}}}

Given:

The perimeter of an isosceles trapezoid is 62 cm.

The length of the fourth side is 10{\text{ cm}}.

Explanation:

Consider the length of the side of trapezoid as x.

Consider the longer side of the trapezoid as x+10.

Perimeter of trapezoid is 62 cm.

\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}

The longer side of the trapezoid is 23{\text{ cm}}.

The semi perimeter of triangle ABE can be obtained as follows,

\begin{aligned}S&= \frac{{a + b + c}}{2}\\&= \frac{{13 + 13 + 10}}{2}\\&= 18\\\end{aligned}

The area of triangle ABE can be obtained as follows,

\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}

The height of the trapezoid can be obtained as follows,

\begin{aligned}{\text{Area} &= 60\\\frac{1}{2}\times b\times h&= 60\\10 \timesh&= 120\\h&= 12\\\end{aligned}

The height of the trapezoid is 12 cm.

The area of parallelogram ABED can be obtained as follows,

\begin{aligned}{\text{Area of ABED}}&= b\times h\\& = 13 \times12\\&= 156{\text{ c}}{{\text{m}}^2}\\\end{aligned}

The area of trapezoid can be calculated as follows,

\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}

The area of trapezoid is \boxed{216{\text{ c}}{{\text{m}}^2}}.

Kindly refer to the image attached.

Learn more:

1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.

2. Learn more about equation of circle brainly.com/question/1506955.

3. Learn more about range and domain of the function brainly.com/question/3412497

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.

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