Question

Solve this question step-by-step please.
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Answer 1

to do this problem we draw perpendiculars from C and D to B and A. we get a rectangle and two triangles.join the two triangles .Now find the area of the new triangle using herons formula.first we find s.

s=(a+b+c)/2=42

then area=

area=336 cm square

next to find height we use the formula area=1/2*base*height

336=1/2*26*height

height=336/13

now we find area of rectangle=52*336/13=1344

hence the total area of trapezium=1344+336=1680cm sq

Hope this helps you

Answer 2

Answer:

From the figure.

In triangle CBM - by Herons formula

$s = a + b + c \div 2$

$28 + 30 + 26 \div 2$

$84 \div 2 = 42$

Now area of triangle by Herons formula

$\sqrt{42(42 - 28)(42 - 30)(42 - 26)} </p><p>$

$</p><p>\sqrt{42 \times 1412 \times 16} </p><p>$

$\sqrt{2 \times 3 \times 7 \times 2 \times 7 \times 4 \times 3 \times 4 \times 4} </p><p>$

$4 \times 2 \times 2 \times 7 \times 3$

$8 \div 42 = 336cm {}^{2}$

Area of parallelogram = Base multiplied by height

$parallelogram = b \times h$

We don't have height

To find height

$\: area \: \: = 1 \div 2 \times base \: \times height$

$336 =1 \div 2 \times 13 \times h$

$336 = 13 \times h$

$336 \div 13 = h$

$25.84 = h$

Now we can find the area of parallelogram

$parallelogram = base \times height$

Parallelogram

$parallelogram \: = 52 \times 25.84$

$= 1343.68cm {}^{2}$

Add bath the areas

$1343.68 + 336 = 1679.68$

Area of trapezium =half multiplied by addinsion of two parallel sides multiplied by height

$area \: of \: trapezium \: = 1 \div 2 \times sum \: of \: two \: parallel \: sides \: \times height \:$

Trapezium

$trapezium \: = 1 \div 2 \times (78 + 52) \times 25.84$

$= 1679.68$