Question

1. Find the areas of given polygons​

Answer 1

in trapezium BGFC;

parallel sides, a & b = 6 cm and 10 cm respectively

height, h = GF = 5 cm

so, ar(trapezium)

$= \frac{h}{2} (a + b) \\ = \frac{5}{2} (6 + 10) = \frac{5}{2} \times 16 = 5 \times 8 \\ = 40 \: {cm}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ... \: (i)$

in parallelogram EFCD;

base, b = CF = 6 cm

height, h = 4.5 cm

so, ar(parallelogram)

= b x h = 6 x 4.5

= 27 cm² ... (ii)

in triangle BAG;

base, b = BG = 10 cm

height, h = AH = 3 cm

so, ar(triangle)

$= \frac{1}{2} \times b \times h \\ = \frac{1}{2} \times 10 \times 3 = \frac{1}{2} \times 30 \\ = 15 \: {cm}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ... \: (iii)$

now,

area of the given polygon

= ar(trapezium) + ar(parallelogram) + ar(triangle)

= 40 cm² + 27 cm² + 15 cm² ... (from i, ii and iii)

= 82 cm².

Hence, area of the given polygon is 82 cm².

Answer 2

Step-by-step explanation:

in trapezium BGFC;

parallel sides, a & b = 6 cm and 10 cm respectively

height, h = GF = 5 cm

so, ar(trapezium)

\begin{gathered} = \frac{h}{2} (a + b) \\ = \frac{5}{2} (6 + 10) = \frac{5}{2} \times 16 = 5 \times 8 \\ = 40 \: {cm}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ... \: (i)\end{gathered}=2h(a+b)=25(6+10)=25×16=5×8=40cm2...(i)

in parallelogram EFCD;

base, b = CF = 6 cm

height, h = 4.5 cm

so, ar(parallelogram)

= b x h = 6 x 4.5

= 27 cm² ... (ii)

in triangle BAG;

base, b = BG = 10 cm

height, h = AH = 3 cm

so, ar(triangle)

\begin{gathered} = \frac{1}{2} \times b \times h \\ = \frac{1}{2} \times 10 \times 3 = \frac{1}{2} \times 30 \\ = 15 \: {cm}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ... \: (iii)\end{gathered}=21×b×h=21×10×3=21×30=15cm2...(iii)

now,

area of the given polygon

= ar(trapezium) + ar(parallelogram) + ar(triangle)

= 40 cm² + 27 cm² + 15 cm² ... (from i, ii and iii)

= 82 cm².

Hence, area of the given polygon is 82 cm².