Question

Find the Area of the figure below, composed of an isoceles trapezoid and one

Answer 1

Answer:

the total area is 15.6 square units

Step-by-step explanation:

hello,

you can  find the total area  dividing the shape into two known shapes

total area= area of the trapezoid +area of the semicircle

then          

step one

find the area of the isosceles trapezoid using

$A=\frac{a+b}{2}*h$

where

a is the smaller base

b is the bigger base

h is theheight

A is the area

let

a=2

b=5

h=4

put the values into the equation

$A=\frac{a+b}{2}*h\\A=\frac{5+2}{2}*4\\A=3.5*4\\A=14$

Step two

find the area of the semicircle

the area of a circle is given by

$A_{c}=\pi \frac{d^{2}}{4}$

but, we need the area of  half circle, we need divide this by 2

$A_{semic}=\frac{ \pi \frac{d^{2}}{4}}{2}\\A_{semic}= \pi \frac{d^{2}}{8}$

now the diameter of the semicircle is 2, put this value into the equation

$A_{semic}= \pi \frac{2^{2}}{8}\\\\A_{semic}= \pi \frac{1}{2}\\ A_{semic}=\frac{\pi }{2}$

find the total area

total area= area of the trapezoid +area of the semicircle

$total\ area= 14+\frac{\pi }{2} \\total\ area=15.6$

so, the total area is 15.6 square units

Have a good day.