1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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.

You might be interested in
Why do systems of nonlinear equations sometimes have more than one solution​
Mice21 [21]

Answer:

System of two linear equations can't have exactly two solutions. Reason is that when we have two straight lines,they can only intersect at one point of intersection,no more. Or let's see if lines are equivalent,then they have infinitely many solutions,because any point on line can be solution for the system.

Step-by-step explanation:

5 0
3 years ago
Which of the following is a perfect square trinomial?
yanalaym [24]
Your answer is D. 16x² - 56xy + 49y².

A perfect square trinomial is the result of a squared binomial, like (a + b)². Using this example, the perfect square trinomial would be a² + 2ab + b², as that is what you get when you expand the brackets.

Therefore, to determine which of these is a perfect square trinomial, we have to see if it can be factorised into the form (a + b)².

I did this by first square rooting the 16x² and 49y² to get 4x and 7y as our two terms in the brackets. We automatically know the answer isn't A or B as you cannot have a negative square number.

Now that we know the brackets are (4x + 7y)², we can expand to find out what the middle term is, so:

(4x + 7y)(4x + 7y)
= 16x² + (7y × 4x) + (7y × 4x) + 49y²
= 16x² + 28xy + 28xy + 49y²
= 16x² + 56xy + 49y².

So we know that the middle number is 56xy. Now we assumed that it was (4x + 7y)², but the same 16x² and 49y² can also be formed by (4x - 7y)², and expanding this bracket turns the +56xy into -56xy, forming option D, 16x² - 56xy + 49y².

I hope this helps!
6 0
3 years ago
Read 2 more answers
The temperature function (in degrees Fahrenheit) in a three dimensional space is given by T(x, y, z) = 3x + 6y - 6z + 1. A bee i
madam [21]

You're looking for the extreme values of T(x,y,z)=3x+6y-6z+1 subject to x^2+y^2+z^2=9. The Lagrangian is

L(x,y,z,\lambda)=3x+6y-6z+1+\lambda(x^2+y^2+z^2-9)

with critical wherever the partial derivatives vanish:

L_x=3+2\lambda x=0\implies x=-\dfrac3{2\lambda}

L_y=6+2\lambda y=0\implies y=-\dfrac3\lambda

L_z=-6+2\lambda z=0\implies z=\dfrac3\lambda

L_\lambda=x^2+y^2+z^2-9=0

Substituting the first three solutions into the last equation gives

\dfrac9{4\lambda^2}+\dfrac9{\lambda^2}+\dfrac9{\lambda^2}=9

\implies\lambda=\pm\dfrac32

\implies x=1,y=2,z=-2\text{ or }x=-1,y=-2,z=2

At these points, we have

T(1,2,-2)=28

T(-1,-2,2)=-26

so the highest temperature the bee can experience is 28º F at the point (1, 2, -2), and the lowest is -26º F at the point (-1, -2, 2).

6 0
3 years ago
4. What is the y-intercept of the line
vagabundo [1.1K]

Answer:

A) (0,0)

Step-by-step explanation:

Plug in 0 for x to solve for y. y=4(0).

4(0)=0, so y=0.

8 0
3 years ago
I need help with this geometry question please
jolli1 [7]
Where’s the question I need to see the problem
3 0
3 years ago
Other questions:
  • Which number is the additive inverse of -4 and 1/4 of a -4 1/4 b -1/4 c 1/ 4 d 4 1/4. What's the answer
    10·1 answer
  • Kali earns $8 per hour. She worked x hours on both Monday and Tuesday. She also worked 5 hours on Thursday. The expression which
    13·1 answer
  • There are 3 marbles (yellow,blue,and green). You pick a marble and flip a coin. How many outcomes are possible?
    6·2 answers
  • What is 1/6 of 42<br> How to solve it
    8·1 answer
  • Which type of traits are found on chromosomes that are unique to one sex, either male or female?
    6·2 answers
  • You manage an ice cream factory that makes three flavors: Creamy Vanilla, Continental Mocha, and Succulent Strawberry. Into each
    8·1 answer
  • Stuck on this question. Any help? ​
    15·1 answer
  • Can someone please help 4x + 2x + 1 = 2x - x + 21
    12·1 answer
  •  In a survey of 1,800 people who owned a certain type of​ car, 990 said they would buy that type of car again. What percent of t
    7·1 answer
  • Free BRAINLESS it could be youea​
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!