Ask question

Ask question

All categories

2 years ago

15

How do you find the area of the shaded region

1 answer:

Amiraneli [1.4K]2 years ago

3 0

well, first off, let's notice that we have a trapezoid with a rectangle inside it, so the rectangle is really "using up" area that the trapezoid already has.

now, if we just get the area of the trapezoid, and then the area of the rectangle alone, and then subtract that area of the rectangle, the rectangle will in effect be making a hole inside the trapezoid's area, and what's leftover, is the shaded section, that part the hole is not touching.

$\bf \textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h&=height\\ a,b&=\stackrel{parallel~sides}{bases} \\\cline{1-2} h&=8\\ a&=16\\ b&=8 \end{cases}\implies A=\cfrac{8(16+8)}{2}\implies A=96 \\\\\\ \stackrel{\textit{area of the rectangle}}{(5\cdot 3)\implies 15}~\hfill \stackrel{~\hfill \textit{shaded area}}{\stackrel{\textit{trapezoid}}{96}~~ - ~~\stackrel{\textit{rectangle}}{15}~~ = ~~81}$

You might be interested in

Given that the rectangle above has an area of 48 square units, find m angle klj. round the answer to the nearest hundreth.

slava [35]

Hello,

tan KLJ=6/8=3/4
=> mes angle KLJ=36.8698976558...°≈36.87 °
Answer B.

8 0

3 years ago

Read 2 more answers

A particle moves on a straight line and has acceleration a(t)=24t+2. Its position at time t=0 is s(0)=3 and its velocity at time

user100 [1]

Answer:

It's position at time t = 5 is 593.

Step-by-step explanation:

The velocity v(t) is the integral of the acceleration a(t)

The position s(t) is the integral of the velocity v(t)

We have that:

The acceleration is:

$a(t) = 24t + 2$

Velocity:

$v(t) = \int {a(t)} \, dt = \int {24t + 2} \, dt = 12t^{2} + 2t + K$

K is the initial velocity, that is v(0). Since V(0) = 13, K = 13

Then

$v(t) = 12t^{2} + 2t + 13$

Position:

$s(t) = \int {s(t)} \, dt = \int {12t^{2} + 2t + 13} \, dt = 4t^{3} + t^{2} + 13t + K$

Since s(0) = 3

$s(t) = 4t^{3} + t^{2} + 13t + 3$

What is its position at time t=5?

This is s(5).

$s(t) = 4t^{3} + t^{2} + 13t + 3$

$s(5) = 4*5^{3} + 5^{2} + 13*5 + 3$

$s(5) = 593$

It's position at time t = 5 is 593.

3 0

2 years ago

For triangle ABC, m(∠A) = 30° and m(∠B)= 115°. Which of the following lists the sides of the triangle from shortest to longest?

Oliga [24]

2 hope this helps you

7 0

2 years ago

Read 2 more answers

You deposit $2000 into an account which pays 4.5% annual intrest compounded quarterly. How long will it take the account to doub

Elan Coil [88]

Answer: She could have the same future value and invest less than $2,000 initially if she could earn more than 64.5 percent interest.

Step-by-step explanation:

6 0

3 years ago

Write -3i + (3/4+2i) - (9/3+3i) as a complex number in standard form

bogdanovich [222]

Answer:

= -3i + (3/4+2i) - (9/3+3i)

= (3/4 - 9/3) + (-3 + 2 -3)i

= -9/4 -4i

4 0

3 years ago