Name: Calculating the Area of Shapes
Uploaded: 2019-07-19
Duration: 20 min 35 s
Description: In this video, we will learn the area of different shapes such as parallelogram, square, rectangle, rhombus, kite, triangle and other combined figures.

Question

Find the area of the pentagon $CHINA,$ if $CN = 12 cm, CJ = 10 cm, CB = 8 cm, CG = 7 cm, HG = 7 cm, IJ = 9 cm$ and $AB = 5 cm$ .

Accepted Answer

Given

$CN = 12 cm, CJ = 10 cm, CB = 8 cm, CG = 7 cm, HG = 7 cm, IJ = 9 cm$ and $AB = 5 cm$

Now

area of $∆ CHG$

$= \frac{1}{2} \times CG \times HG = \frac{1}{2} \times 7 \times 7 = \frac{49}{2} {cm}^{2} . . (i)$

area of $∆ CBA$

$= \frac{1}{2} \times CB \times AB = \frac{1}{2} \times 8 \times 5 = \frac{40}{2} = 20 {cm}^{2} . . . (ii)$

area of $∆ IJN$

$= \frac{1}{2} \times JN \times IJ$

$∵ J N = CN - CJ = 12 cm - 10 cm = 2 cm$

$∴$ area of $∆ IJN$

$= \frac{1}{2} \times 2 \times 9 = 9 c m^{2} . . . (iii)$

area of $ABN = \frac{1}{2} \times AB \times BN$

$= \frac{1}{2} AB \times (CN - CB) = \frac{1}{2} \times 5 \times (12 - 8) {cm}^{2} = \frac{1}{2} \times 5 \times 4 = 10 {cm}^{2} . . . (iv)$

area of trapezium $GHIJ$

$= \frac{1}{2} (GH + IJ) \times GJ = \frac{1}{2} (GH + IJ) \times (CJ - CG) = \frac{1}{2} (7 + 9) \times (10 - 7) {cm}^{2} = \frac{1}{2} \times 16 \times 3 {cm}^{2} = 24 {cm}^{2} . . . (v)$

Here total area of pentagon $CHINA$

$=$ Area of $∆ CHG +$ area of $∆ CBA +$ area of $∆ IJN +$ area of $∆ ABN +$ area of trapezium $GHIJ$

$= \frac{49}{2} + 20 + 9 + 10 + 24 {cm}^{2}$

from equation $(i), (ii), (iii), (iv), (v)$

$= \frac{175}{2} {cm}^{2} = 87.5 {cm}^{2}$

Therefore, total area of pentagon is $87.5 {cm}^{2}$

Find the area of the pentagon $CHINA,$ if $CN = 12 cm, CJ = 10 cm, CB = 8 cm, CG = 7 cm, HG = 7 cm, IJ = 9 cm$ and $AB = 5 cm$ .

Important Questions on Mensuration-I (Plane Figures)

Learn and Prepare for any exam you want !

Find the area of the pentagon CHINA, if CN=12 cm, CJ=10 cm, CB=8 cm, CG=7 cm, HG=7 cm, IJ=9 cm and AB=5 cm.

Important Questions on Mensuration-I (Plane Figures)

Learn and Prepare for any exam you want !

Find the area of the pentagon $CHINA,$ if $CN = 12 cm, CJ = 10 cm, CB = 8 cm, CG = 7 cm, HG = 7 cm, IJ = 9 cm$ and $AB = 5 cm$ .