What is the area of the trapezoid shown below?

Hello there!

Your answer is 180 units²

Step-by-step explanation:

[tex] \large \boxed{ \mathsf{ \frac{1}{2} \times sum \: of \: two \: parallel \: \times height}}[/tex]

The formula in the box is an area of trapezoid formula. We know the sum of two parallel lines which is 15 because 7+4 = 11 + 4 = 15

another 4 comes from parallel side. If both sides are parallel, they have same length.

The only thing that is missing is the height. The height can be found by using Pythagorean Theorem as you notice a right-angle triangle when splitting in half.

[tex] \large \boxed{ {a}^{2} + {b}^{2} = {c}^{2} }[/tex]

The formula in the box is Pythagorean Theorem for finding a length of right-angle triangle.

Given where a is opposite, b is adjacent and c is hypotenuse. (Note that c must be hypotenuse.)

Our a is missing

Our b is 7

Our c is 25.

From the formula and given lengths:

[tex] \large{ {a}^{2} + {7}^{2} = {25}^{2} } \\ \large{ {a}^{2} + 49 = 625} \\ \large{ {a}^{2} = 625 - 49} \\ \large{ {a}^{2} = 576} \\ \large{a = 24}[/tex]

Therefore, our opposite is 24. Since our opposite equals the height of a trapezoid. We can proceed with the trapezoid formula.

[tex] \large{ \frac{1}{2} \times 15 \times 24 = 15 \times 12 = 180 } \\ \large{180}[/tex]

Therefore, the area of trapezoid is 180 units²

We can also use another method to find the area by adding up between area of triangle and area of Rectangle.

Our rectangle formula is length × width. We know width which is 4 and our length is 24 from opposite side of triangle which equal to the length of rectangle.

Length × Width = 24 × 4 = 96

Hence, the area of Rectangle is 96.

Next, we find the area of triangle which is 1/2 × base × height.

Our base is 7 and height is the opposite side of triangle which is 24.

Therefore, the area of triangle is 1/2 × 7 × 24 = 7 × 12 = 84

If we add the area of triangle and rectangle up each other, we will get the area of trapezoid for this problem which is 96 from rectangle and 84 from triangle. Therefore, 96+84 = 180 units²

A simple interest loan of
$4,000 was repaid at the end
of 3 years with a check for
$4,972. What annual rate of
interest was charged?

(copy nd paste)
Sue and Cathy have $20 left for a cab fare home. The cab fare is $3 per mile plus a $2 fixed charge. What is the maximum number of miles they will be able to travel in the cab?

The base of a parallelogram is 3.2 centimeters and the height is 1.8 centimeters. What is the area of the parallelogram? Do not round your answer.

A = ____cm 2

here are some questions that need answering:
thnx!

Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match the multiplication expressions to the exponential expressions.

5x5x5x5 - 6x6x6 - 3x3x3x3x3x3 - 4x4x4x4x4 - 5x5x5x5x5

3^6 ----------> ______
4^5 ----------> ______
6^3 ----------> ______
5^4 ----------> ______

help me please with this

HELPP ITS DUE TODAY AND MY BRAIN ISNT WORKING
question
-Write a statistical question.

don't laugh

Find three consecutive odd numbers whose sum is 81. *

PLEASE HELP WITH THESE !!
ILL TRY TO MARK BRAINLIEST !!

What is this answer (please)

Thank you. The Picture is there. :)

-10=5 - 3s
Can you help me

Select the correct answer from each drop-down menu.
A sports apparel company surveyed the market about the size of T-shirts people most frequently buy, small, medium, large, or extra-large. The
table shows the survey results.
T-Shirt Size Number of responses
small
11
mediurn
37
large
83
extra-large
19
To help Its sales, the company should focus on producing size
T-shirts. Approximately % of T-shirts the company
makes should be medium and large T-shirts to match the market preference. If the total number of T-shirts sold in a month is 45,000,
of these will likely be size small.

Jada is 13 5/6
years old. Sheila is 1 1/3
years older than Jada and Jane is 1 1/4
years older than Sheila. How old is Jane?

Please help me I need this in like 10min

A circular garden has a circumference of 138 yards. Lars is digging a straight line along a diameter of the garden at a rate of 11 yards per hour. How many hours will it take him to dig across the garden? Use 3.14 for π and round the diameter to the nearest whole number, if necessary

1⁄7 + 1⁄2 + 3⁄4 =???

Make a number line and show all values of x. x≤2 and x< -5

Please help me do it on a paper.
Ladder method for
5, 8 , 10

CAN SOMEONE PLEASE HELP ME WITH THIS PLEASE!!!

Which of these are statistical questions? You can pick more than one answer


Question 1: How many minutes does it usually take you to get from home to work?

Question 2: During the past year did you work for more than 50 weeks?

Question 3: During the past year how many hours did you usually work each week?

Question 4: How many extra hours did you work each week?

2(x-4)+3=7 which of these is x 4,6,7,8

Find the value of x help me

Deandre has a bookcase with k shelves. There are 13 books on each shelf. Using k , write an expression for the total number of books.

PLZ HELP ME ON THIS THANK YOU SO MUCH!

an angle measure 23 degrees more than the measure of its complementary angle . what is the measure

-1= p - 1
Can you help me?

When given a system of equations in​ slope-intercept form, is graphing or substitution the most efficient method to​ solve? Explain.
Choose the best answer below.
A.
Substitution is the only method that should be used if the answer involves integer values. If the answer involves values that are not​ integers, graphing would be more efficient because an exact answer can be obtained. It is easier to read graphs when the point of intersection does not occur at integer values.
B.
Graphing is the only method that would be appropriate to use here because it is not possible to use the substitution method if both equations are in​ slope-intercept form.
C.
Substitution is the only method that would be appropriate to use here because it is not possible to use the graphing method if both equations are in​ slope-intercept form.
D.
Graphing and substitution are appropriate to use if the answer involves integer values. If the answer involves values that are not​ integers, substitution would be more efficient because an exact answer can be obtained. It can be difficult to read graphs if the intersection point does not have integer values so this would be an inefficient method to solve with.

PLEASE HELPPPPP

Simplify the expressions by combining like terms

1.5r - 3r + 8r + 2.5r

I really need help with this, please help