In a quadrilateral ABCD,AB = 9 , cm,BC = 40 , | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) $1$. Join $AC$ to divide the quadrilateral $ABCD$ into two triangles: $	riangle ABC$ and $	riangle ADC$.$2$. In right-angled $	riangle ABC$,by

Vedclass · Accepted Answer

$306$

Vedclass · Answer

(A) $1$. Join $AC$ to divide the quadrilateral $ABCD$ into two triangles: $	riangle ABC$ and $	riangle ADC$.$2$. In right-angled $	riangle ABC$,by Pythagoras theorem: $AC^2 = AB^2 + BC^2 = 9^2 + 40^2 = 81 + 1600 = 1681$. Thus,$AC = \sqrt{1681} = 41 \, cm$.$3$. Area of $	riangle ABC = \frac{1}{2} 	imes 	ext{base} 	imes 	ext{height} = \frac{1}{2} 	imes 40 	imes 9 = 180 \, cm^2$.$4$. For $	riangle ADC$,the sides are $a = 41 \, cm$,$b = 28 \, cm$,and $c = 15 \, cm$. Semi-perimeter $s = \frac{41 + 28 + 15}{2} = \frac{84}{2} = 42 \, cm$.$5$. Area of $	riangle ADC = \sqrt{s(s-a)(s-b)(s-c)} = \sqrt{42(42-41)(42-28)(42-15)} = \sqrt{42 	imes 1 	imes 14 	imes 27} = \sqrt{(14 	imes 3) 	imes 14 	imes (9 	imes 3)} = \sqrt{14^2 	imes 3^2 	imes 3^2} = 14 	imes 3 	imes 3 = 126 \, cm^2$.$6$. Total area of quadrilateral $ABCD = 	ext{Area}(	riangle ABC) + 	ext{Area}(	riangle ADC) = 180 + 126 = 306 \, cm^2$.

In a quadrilateral $ABCD$,$AB = 9 \, cm$,$BC = 40 \, cm$,$CD = 28 \, cm$,$DA = 15 \, cm$,and $\angle B = 90^{\circ}$. Find its area. (in $, cm^2$)

Similar Questions

$A$ rhombus-shaped sheet with a perimeter of $40 \, cm$ and one diagonal of $12 \, cm$ is painted on both sides at the rate of $Rs \, 5$ per $cm^2$. Find the cost of painting (in $Rs$).

The sides of $\Delta PQR$ measure $13 \, cm$, $14 \, cm$, and $15 \, cm$. Find its area in $cm^2$.

The edges of a triangular board are $6 \, cm$,$8 \, cm$,and $10 \, cm$. The cost of painting it at the rate of $9$ paise per $cm^2$ is:

The ratio of the measures of the sides of a triangle is $3: 4: 6$. If the semiperimeter of the triangle is $39 \, cm$,the measure of the longest side of the triangle is ............ $cm$.

Area of a right triangle $=$ ...........

Vedclass Test Series

Exam Paper Generator

Online Exam Module