Question

plZ solved this two question plZ plz​

Answer 1

Question 6

Given : ABCD is a parallelogram in which DF = BE = 12 m and AC diagonal is 36 m.

To Find : Area of parallelogram ABCD

Solution :

Area of Parallelogram ABCD = Area of ∆ ABC + Area of ∆ ADC

In ∆ ABC

BE is perpendicular to AC

BE is altitude which is 12 m

AC is base which is 36 m

Area of ∆ ABC = $\dfrac{1}{2}\times Base \times Height$

Area of ∆ ABC = $\dfrac{1}{2}\times 36 \times 12$

Area of ∆ ABC = (18 × 12) m²

Area of ∆ ABC = 216 m²

Similarly in ∆ ADC

DF is a altitude which is 12 m

AC is a base which is 36 m

Means the area of ∆ ADC is also 216 m²

Area of Parallelogram ABCD = Area of ∆ ABC + Area of ∆ ADC

Area of Parallelogram ABCD = 216 + 216 = 216(1+1)

Area of Parallelogram ABCD = 2{216} = 432 m²

Area of Parallelogram ABCD is 432 m².

Question 7

Method 1

Given : AB = 14 m , BC = 10 m , DC = 22 m

Construction : Construct AO perpendicular to DC having a length equal to BC.

(Refer image 2)

Solution :

In ∆ AOD

AO, altitude of length 10 m

DO, base of length 8 m

Area of ∆ AOD = $\dfrac{1}{2} \times Base \times Height$

Area of ∆ AOD = $\dfrac{1}{2} \times AO \times DO$

Area of ∆ AOD = $\dfrac{1}{2} \times 8 \times 10$

Area of ∆ AOD = 40 m²

ABCO is a rectangle in which

AO = 10 m

AB = 14 m

Area of rectangle = length × breadth

Area of rectangle = AB × AO

Area of rectangle = (14 × 10) m²

Area of rectangle = 140 m²

Area of quadrilateral = area of ∆ AOD + area of rectangle ABCO

Area of quadrilateral ABCD = (40 + 140) m²

Area of quadrilateral ABCD is 180 m²

Method 2

Given : AB = 14 m , BC = 10 m , DC = 22 m

Construction :

1. Construct AO $\perp$ DC

2. Construct a diagonal AC forming ∆ ADC

(refer image 3 for figure)

Solution :

In ∆ ABC

Area of ∆ ABC = $\dfrac{1}{2} \times Base \times Height$

Area of ∆ ABC = $\dfrac{1}{2} \times 14 \times 10$

Area of ∆ ABC = 70 m²

In ∆ ADC

AO is altitude of 10 m

DC is base of 22 m

Area of ∆ ADC = $\dfrac{1}{2} \times Base \times Height$

Area of ∆ ADC = $\dfrac{1}{2} \times 10 \times 22$

Area of ∆ ABC = $10 \times 11$

Area of ∆ ADC is 110 m².

Area of quadrilateral = area of ∆ ABC+ area of ∆ ADC

Area of quadrilateral = (70 + 110) m²

Area of quadrilateral ABCD is 180 m².