Find the area of the figure with Heron’s formula

Mathematics

1 answer:

Anna11 [10]3 years ago

7 0

Answer:

735 cm²

Step-by-step explanation:

The figure is a trapezium .The area of the triangle section can be calculated using the Heron's formula.

The other part of the figure will be a square of sides 21 cm by 21 cm

Area of the square section

Area = l²

Area = 21* 21 = 441 cm²

Area of the triangle using Heron's formula

Sides of the triangle are ;

a= 28 cm

c= 35 cm

b = 21 cm -----height of the trapezium

The Heron's formula is given as;

$A=\sqrt{s( s-a)(s-b )(s-c )}$

where s is half the perimeter of the triangle

Perimeter of the triangle is given as ;

P= 35 + 28 + 21 =84 cm

s= 84/2 = 42 cm

$A=\sqrt{42*(42-21 )*(42-35 )*(42-28 )} \\\\A=\sqrt{42*(21 )*(7 )*( 14)} \\\\A=\sqrt{86436} \\\\A=294\\\\$

Total area = 294 + 441 = 735 cm²

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