Question

5. Find the area of a wall shown in Fig. 14.17.​

Answer 1

Answer:

first area of rectangle = 100×60 =6000m

area of triangle ️= 1/2×base×height = 1/2×100×60= 3000

area = 6000+3000 = 9000m

Answer 2

Analysis:

• According to the diagram of the wall, it has been visualised as two parts. A rectangular part below a triangular part.
• The height and the base length of the triangular part are 15 m and 100 m, respectively.
• The length of the rectangular part is 100 m and it's breadth is 60 m.

What to do?

• We've to find the area of the wall.

Formulae used:

• Area of triangle = ½ (bh) sq.units
• Area of rectangle = lb sq.units

Solution:

Look at the attachment! As we are asked to find the area of the wall, we can say that the sum of the area of triangular part and the area of rectangular part equals the area of complete wall. So, first we shall be calculating the areas of triangle and rectangle. And then, summing up both the measures, which results to required answer. Let's do it !!

$\:$

Area of triangular part:

$\:\:\:\:\:\longmapsto{\sf{\dfrac{1}{2}bh\:sq.units}}$

(Substituting the measures)-

$\\\:\:\:\:\:\longmapsto{\bf{\dfrac{1}{2}\times 100\times 15}}$

$\\\:\:\:\:\:\longmapsto{\bf{\dfrac{1}{\cancel{2}}\times \cancel{1500}}}$

$\\\:\:\:\:\:\longmapsto{\bf{1\times 750}}$

$\\\:\:\:\:\:\longmapsto\underline{\bf{\blue{750\:m^2}}}$

$\:$

Area of rectangular part:

$\:\:\:\:\:\longmapsto{\sf{lb\:sq.units}}$

(Substituting the measures)-

$\\\:\:\:\:\:\longmapsto{\bf{100\times 60}}$

$\\\:\:\:\:\:\longmapsto\underline{\bf{\pink{6000\:m^2}}}$

$\:$

*Area of the wall:

$\leadsto{\sf{Area_{(Triangle)}+Area_{(Rectangle)}}}$

$\\\:\:\:\:\:\longmapsto{\bf{750+6000}}$

$\:\:\:\:\:\longmapsto\star\:{\boxed{\frak{\red{6750\:m^2}}}}$

$\\\therefore\underline{\sf{The\:area\:of\:the\:wall\:is\:\bf{6,750\:m^2}\sf{.}}}$

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Some formulas for AREA:-

$\:\:\:\sf{\bullet\: Trapezium=\dfrac{1}{2}h(sum\: of\: parallel\:sides)\:sq.units}$

$\:\:\:\sf{\bullet\: Parallelogram=bh\:sq.units}$

$\:\:\:\sf{\bullet\: Rhombus=\dfrac{1}{2}d_1d_2\:sq.units}$

$\:\:\:\sf{\bullet\: Square=a^2\:sq.units}$

$\:\:\:\sf{\bullet\: Circle=\pi r^2\:sq.units}$

$\:\:\:\sf{\bullet\: Semi\: circle=\dfrac{1}{2}\pi r^2\:sq.units}$