Question

in adjecent quadrilateral abcd ac is the diagonal of length 36cm, be and df perpendicular from b and d to ac are 8 cm and 12 cm respectively find area of quadrilateral ​

Answer 1

Question:

In the adjacent Quadrilateral ABCD, AC is the diagonal of length 36cm, BE and DF perpendicular from B and D to AC are 8cm and 12cm respectively. Find the area of the quadrilateral.

Answer:

Area of the given Quadrilateral = 860 cm²

Step-by-step explanation:

In the given figure we have two triangles, ∆ADC and ∆ABC.

The ∆ ADC, Base = 36cm and height = 12cm

Now, let's calculate the area of the ∆ ADC

$\bf Area \ of \ \triangle ADC = \dfrac{1}{2} BASE \times HEIGHT$

$\sf Area \ of \ \triangle ADC = \dfrac{1}{2} 36 \times 12$

$\sf Area \ of \ \triangle ADC = 18 \times 12$

$\sf Area \ of \ \triangle ADC = 216cm^2$

The ∆ ABC, Base = 36cm and Height = 8cm

Now, let's calculate the area of the ∆ ABC

$\bf Area \ of \triangle ABC = \dfrac{1}{2} BASE \times HEIGHT$

$\sf Area \ of \ \triangle ABC = \dfrac{1}{2} 36 \times 8$

$\sf Area \ of \ \triangle ABC = 36 \times 4$

$\sf Area \ of \ \triangle ABC = 144cm^2$

Area of Quadrilateral = ADC + ABC

Area of Quadrilateral = 216cm² + 144cm² = 360cm²

Answer 2

Answer:

Given :-

in adjecent quadrilateral abcd ac is the diagonal of length 36cm, be and df perpendicular from b and d to ac are 8 cm and 12 cm respectively find area of quadrilateral

To Find :-

Area

Solution :-

At first we have to find Area of ∆ADC

∆ADC = ½ × 36 × 12

∆ADC = 18 × 13

∆ADC = 216 cm²

Therefore,

the Base will remain same and height be decreased by 4

Hence,

Base = 36 cm

Height = 8 cm

∆ABC = ½ × 36 × 8

∆ABC = 36 × 4

∆ABC = 144 cm²

Total area = 216cm² + 144cm² = 360cm²