Question

What is the area of the trapezoid shown below?

Answer 1

180 square units

Explanation:

`Height \: of \: trapezoid \\ h = \sqrt{ {25}^(2) - {7}^(2) } \\ = √(625 - 49) \\ = √(576) \\ h = 24 \: units \\ \\ b_1 = 4 \:units \\ b_2 = 7 + 4 = 11 \:units \\ \\ Area \: of \: trapezoid \\ = (1)/(2) (b_1 + b_2) * h \\ \\ = (1)/(2) (4 + 11) * 24 \\ = 15 * 12 \\ \red{ \boxed{ \bold{area \: of \: trapezoid = 180 \: {units}^(2)}}} \\`

Answer 2

we will use Pythagoras theorum to find out area of that right angled triangle .

Base = 7units

hypotenuse = 25units

perpendicular= ?

Pythagoras theorem = >

base²+perpendicular ²= hypotenuse ²

(7)²+(p)²= (25)²

49+(p)²=625

(p)²= 625-49

(p)²=576

p = 24units

area of triangle =

`(1)/(2</strong><strong>)</strong><strong>h</strong><strong>+</strong><strong>b</strong><strong>`

`(1)/(2) </strong><strong>2</strong><strong>4</strong><strong>+</strong><strong>7</strong><strong>`

area of triangle = 31units ²

length of rectangle = 24units

breadth= 4units

area of rectangle = l×b

area of rectangle = 4×24

area of rectangle = 28 units .

so total area = area of triangle + area of rectangle

= 31+28

answer = 59units²