Question

One diagonal of a quadrilateral is 18cm and the lengths of the perpendicular to it from the other two vertices are 7cm and 10cm respectively. Find the area of the quadrilateral.      ​

Answer 1

Answer:

Area of quadrilateral = 153$cm^{2}$

Step-by-step explanation:

According to the information provided in the question it is given as

One diagonal of a quadrilateral = 18 cm

Lengths of the perpendicular to it from the other two vertices are 7 cm and 10 cm respectively.

We need to find the area of the quadrilateral.      ​

First understand the meaning or definition of quadrilateral

A quadrilateral is a closed shape and a type of polygon that has four sides, four vertices and four angles. It is formed by joining four non-collinear.

Quadrilateral Formula = 1/2 x diagonals length x ( sum of the height of two triangles )

Here diagonal length =l = 18 cm

         height =h= 7 cm, 10 cm

Hence by substituting the values we get the area

[tex]A = \frac{1}{2} \times 18 \times (7+10)\\ A = \frac{1}{2} \times 18 \times (17)\\ A = 9\times 17\\ A = 153cm^{2} [/tex]

Hence area of quadrilateral is 153$cm^{2}$

Answer 2

Given :-

• One diagonal of a quadrilateral is 18 cm and the lengths of the perpendicular to it from the other two vertices are 7 cm and 10 cm respectively.

To Find :-

• What is the area of quadrilateral.

Formula Used :-

$\clubsuit$ Area Of Quadrilateral Formula :

$\footnotesize \bigstar \: \: \sf\boxed{\bold{\pink{Area_{(Quadrilateral)} =\: \dfrac{1}{2} \times (Length\: of\: Diagonal) \times (Sum\: of\: Height)}}}\: \: \: \bigstar$

Solution :-

Given :

• Diagonal of Length (d) = 18 cm
• Height (h₁ , h₂) = 7 cm and 10 cm

According to the question by using the formula we get,

$\footnotesize \implies \sf\bold{\blue{Area_{(Quadrilateral)} =\: \dfrac{1}{2} \times (Length\: of\: Diagonal) \times (Sum\: of\: Height)}}$

$\implies \bf Area_{(Quadrilateral)} =\: \dfrac{1}{2} \times d \times (h_1 + h_2)$

$\implies \sf Area_{(Quadrilateral)} =\: \dfrac{1}{2} \times 18 \times (7 + 10)$

$\implies \sf Area_{(Quadrilateral)} =\: \dfrac{1}{2} \times 18 \times 17$

$\implies \sf Area_{(Quadrilateral)} =\: \dfrac{1}{2} \times 306$

$\implies \sf Area_{(Quadrilateral)} =\: \dfrac{1 \times 306}{2}$

$\implies \sf Area_{(Quadrilateral)} =\: \dfrac{\cancel{306}}{\cancel{2}}$

$\implies \sf Area_{(Quadrilateral)} =\: \dfrac{153}{1}$

$\implies \sf\bold{\red{Area_{(Quadrilateral)} =\: 153\: cm^2}}$

$\sf\bold{\purple{\underline{\therefore\: The\: area\: of\: quadrilateral\: is\: 153\: cm^2\: .}}}$

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