Question

Find the area of pentagon ABCDE (Fig. 5) in which BF IAC, CG I AD and EH 1 AD,
such that AC = 8 cm, AD = 15 cm, BF = 3 cm, CG = 7 cm and EH = 5 cm.
​

Answer 1

Area of the pentagon is $105 \ cm^2$

Explanation:

It is given that AC = 8 cm, AD = 15 cm, BF = 3 cm, CG = 7 cm and EH = 5 cm.

From the figure the area of the pentagon can be determined using the formula,

​ Area of the pentagon ABCDE = Area of ΔABC + Area of ΔACD + Area of ΔAED

Area of ΔABC = $\frac{1}{2} \times b \times h= \frac{1}{2} \times AC \times BF$

Substituting the values, we get,

Area of ΔABC = $\frac{1}{2} \times 8 \times 3=12 \ cm^2$

Similarly,

Area of ΔACD = $\frac{1}{2} \times AD \times CG=\frac{1}{2} \times 15 \times 7= 52.5 \ cm^2$

Area of ΔAED = $\frac{1}{2} \times AD \times EH=\frac{1}{2} \times 15 \times 5= 37.5 \ cm^2$

Now, Substituting all the values of the triangles in the formula, we have,

Area of the pentagon ABCDE = Area of ΔABC + Area of ΔACD + Area of ΔAED

Area of the pentagon ABCDE = $12+52.5+37.5=105 \ cm^2$

Thus, the area of the pentagon is $105 \ cm^2$

Learn more:

(1) brainly.in/question/2837567

(2) brainly.in/question/2315817