All categories

3 years ago

ABCD is a trapezium in which AB ∥ CD, AD ⊥ DC, AB = 4 cm, BP = 7 cm and DC = 25 cm, then area of the trapezium is 45.

Mathematics

1 answer:

Elza [17]3 years ago

8 0

Question:

ABCD is a trapezium in which AB ∥ CD, AD ⊥ DC, AB = 4 cm, BP = 7 cm and DC = 25 cm, then area of the trapezium is ____.

Answer:

101.5cm²

Step-by-step explanation:

The figure for the trapezium ABCD is attached to this response.

To find the area of the trapezium, we use the formula for calculating the area of a trapezium given as follows;

A = $\frac{1}{2}$ x (a + b) x h ------------------(i)

Where;

A = area of the trapezium

a and b are the parallel sides of the trapezium

h = height of the trapezium.

As shown in the figure,

<em>AB and CD are parallel</em>

Therefore, we can say that;

a = AB

b = CD

Also, from the figure,

<em>The height of the trapezium is BP</em>

Therefore, we can say that;

h = BP

We know that;

a = AB = 4cm

b = CD = 25cm

h = BP = 7cm

Substitute these values of a, b and h into equation (i) as follows;

A = $\frac{1}{2}$ x (4 + 25) x 7

A = $\frac{1}{2}$ x (29) x 7

A = 101.5

Therefore, the area of the trapezium is 101.5cm²

You might be interested in

Use DeMoivre's Theorem to find the indicated power of the complex number. Write the answer in rectangular form.

slava [35]

Answer:

After solving the power:

$\bold{2(cos60^\circ+isin60^\circ)}$

Rectangular form:

$\bold{1+i\sqrt3}$

Step-by-step explanation:

Given the complex number:

$2(cos20^\circ+isin20^\circ)^3$

To find:

The indicated power by using De Moivre's theorem.

The complex number in rectangular form.

Rectangular form of a complex number is given as $a+ib$ where a and b are real numbers.

Solution:

First of all, let us have a look at the De Moivre's theorem:

$(cos\theta+isin\theta )^n=cos(n\theta)+isin(n\theta )$

First of all, let us solve:

$(cos20^\circ+isin20^\circ)^3$

Let us apply the De Moivre's Theorem:

Here, n = 3

$(cos20^\circ+isin20^\circ)^3 = cos(3 \times 20)^\circ+isin(3 \times 20)^\circ\\\Rightarrow cos60^\circ+isin60^\circ$

Now, the given complex number becomes:

$2(cos60^\circ+isin60^\circ)$

Let us put the values of $cos60^\circ = \frac{1}{2}$ and $sin60^\circ = \frac{\sqrt3}{2}$

$2(\dfrac{1}{2}+i\dfrac{\sqrt3}2)\\\Rightarrow (2 \times \dfrac{1}{2}+i\dfrac{\sqrt3}2\times 2)\\\Rightarrow \bold{1 +i\sqrt3 }$

So, the rectangular form of the given complex number is:

$\bold{1+i\sqrt3}$

3 0

3 years ago

Which equation represents a line that passes through (2-3) and has a slope of 5?

larisa [96]

Answer:

y=5x-13

Step-by-step explanation:

y-y1=m(x-x1)

y-(-3)=5(x-2)

y+3=5(x-2)

y=5x-10-3

y=5x-13

6 0

4 years ago

The ages of a group of 135 randomly selected adult females have a standard deviation of 18.3 years. Assume that the ages of fema

NeTakaya

Answer:

Therefore, the number of female statistics student ages that must be obtained in order to estimate the mean age of all female statistics student is 3625 female statistics student

Step-by-step explanation:

Here, we have

$n = \left (\frac{(z_{\alpha/2}) (\sigma) }{E} \right )^{2}$

Where:

n = Required sample size

σ = Standard deviation = 18.3

E = Margin of error = 1/2 year

$z_{\alpha /2}$ = Critical score from the confidence level = 1.645

Therefore,

$n = \left (\frac{(1.645) (18.3) }{\frac{1}{2} } \right )^{2} = 3624.88$

Therefore, the number of female statistics student ages that must be obtained in order to estimate the mean age of all female statistics student = 3625 female statistics student.

3 0

3 years ago

Need help with this math question 30 points correct answers only pls

Likurg_2 [28]

its the third answer

Step-by-step explanation:

and its only 5 points not 30

3 0

3 years ago

Read 2 more answers

Please help me solve this: 6 1/3 + k + 3 5/6 + 5 1/2 = 26 1/6

attashe74 [19]

6 1/3 + k + 3 5/6 + 5 1/2 = 26 1/6
Add your fractions
6 1/3 + 3 5/6 + 5 1/2 = 15 2/3
now You need to isolate k on one side of the equation by using the subtraction method of equality.
k + 15 2/3 = 26 1/6
k = 10 1/2

Hope this helps

I had to edit

5 0

4 years ago

Read 2 more answers