Name: Area of a Quadrilateral and Rhombus
Uploaded: 2019-07-19
Duration: 8 min 51 s

Question

Nazma’s sister has a trapezium shaped plot. Divide it into three parts as shown in figure. If $h = 10 cm, c = 6 cm, b = 12 cm, d = 4 cm$ , find the values of each of its parts separately and add to find the area $W X Y Z$ . Verify it by putting the values of $h, a$ and $b$ in the expression of area of $W X Y Z = h \frac{(a + b)}{2}$

Accepted Answer

Given, a trapezium shaped plot is divided into three parts as shown in figure. In that, $h = 10 cm, c = 6 cm, b = 12 cm, d = 4 cm$ .

We have to find the values of each of its parts separately and add to find the area $W X Y Z$ .

Also, we have to verify it by putting the values of $h, a$ and $b$ in the expression of area of $W X Y Z = h \frac{(a + b)}{2}$

We know that, area of triangle $= \frac{1}{2} \times base \times height$

And, area of rectangle $= length \times breadth$

Now, area of $∆ W P Z = \frac{1}{2} c h = \frac{1}{2} \times 6 \times 10 = 30 {cm}^{2}$

And, area of $∆ X Q Y = \frac{1}{2} d h = \frac{1}{2} \times 4 \times 10 = 20 {cm}^{2}$

And, area of rectangle $P Q Y Z = b h = 12 \times 10 = 120 {cm}^{2}$

So, Area of trapezium $W X Y Z = \frac{1}{2} c h + b h + \frac{1}{2} d h = 30 + 20 + 120 = 170 {cm}^{2}$ .... (1)

Also given that, Area of trapezium $W X Y Z = h \frac{(a + b)}{2} = 10 \frac{(22 + 12)}{2} = 5 \times 34 = 170 {cm}^{2}$ .... (2)

Hence, from (1) and (2) it is verified.

Important Questions on Mensuration

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Nazma’s sister has a trapezium shaped plot. Divide it into three parts as shown in figure. If h=10 cm, c=6 cm, b=12 cm, d=4 cm, find the values of each of its parts separately and add to find the area WXYZ. Verify it by putting the values of h, a and b in the expression of area of WXYZ=ha+b2

Important Questions on Mensuration

Learn and Prepare for any exam you want !