Question

Find area of each trapezium.

Answer 1

Answer:

Question :-

$: \rightarrowtail$ Find the area of each trapezium.

Given :-

Trapeziums with dimensions are given

(I) Dimensions of First Trapezium -

• First side (a) = 3cm.
• Second side (b) = 7cm.
• Height (h) = 4cm.

ii) Dimensions of Second Trapezium -

• First side (a) = 11cm.
• Second side (b) = 14cm.
• Height (h) = 10cm.

iii) Dimensions of Third Trapezium -

• First side (a) = 12cm.
• Second side (b) = 20cm.
• Height (h) = 7cm.

To Find :-

We need to find the areas of the given three trapeziums.

Solution :-

We know the formula for finding the area of a Trapezium with sides a and b and height h.

${\bold {\boxed{Area\;of\;Trapezium =\frac {1}{2}(a+b)\times Height.}}}$

• Putting the values of a, b and h in the above formula for finding the areas of trapeziums.

⠀

⠀

⠀

___________________________________

___________________________________

a)

$\rightarrow Area\;of\;Trapezium =\frac {1}{2}(a+b)\times H.$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ $\quad = {\frac {1}{2}(3+7)\times 4.}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ $\quad = 5\times 4.$

$\rightarrow \bold {Area\;of\;Trapezium = 20cm^2}$

⠀

⠀

⠀

___________________________________

b)

$\rightarrow Area\;of\;Trapezium =\frac {1}{2}(a+b)\times H.$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ $\quad = {\frac {1}{2}(11+14)\times 10.}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ $\quad = 25\times 5.$

$\rightarrow \bold {Area\;of\;Trapezium = 125cm^2}$

⠀

⠀

⠀

___________________________________

c)

$\rightarrow Area\;of\;Trapezium =\frac {1}{2}(a+b)\times H.$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ $\quad = {\frac {1}{2}(12+20)\times 7.}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ $\quad = 16\times 7.$

$\rightarrow \bold {Area\;of\;Trapezium = 112cm^2}$

⠀

⠀

⠀

___________________________________

___________________________________

___________________________________

Answer 2

$(a) \: a = 3cm \\ \\ b = 7cm \\ \\ h = 4cm \\ \\ area \: = \frac{a + b}{2} \times h \\ \\ area = \frac{3 + 7}{2} \times 4 \\ \\ area = \frac{10}{2} \times 4 \\ \\ area \: = 5 \times 4 \\ \\ area \: = 20 {cm}^{2}$

$(b) \: \: a = 14 \\ \\ b = 11 \\ \\ h = 10 \\ \\ area = \frac{14 + 11}{2} \times 10 \\ \\ area = 15 \times 5 \\ \\ area = 75 {cm}^{2}$

$(c) \: a = 12 \\ \\ b = 20 \\ \\ h = 7 \\ \\ area = \frac{12 + 20}{2} \times 7 \\ \\ area = \frac{32}{2} \times 7 \\ \\ area = 16 \times 7 \\ \\ area = 112 {cm}^{2}$