Question

ABCD is a rectangle.Area of triangle AP B is 12 square cm. What is the area of the rectangle?​

Answer 1

→Answer ;

Area of the rectangle ABCD=12×7=84sqcm.

Let AP=x cm. So, PB=(12−x) cm.

Area of shaded region =0.4×84=33.6 sq cm.

Area of triangle EAP=0.5×5×x=2.5x sq cm

Area of triangle CPB=0.5×7×(12−x)=42−3.5x sq cm

Sum of the area of triangles EAP and CPB = area of shaded region

2.5x+42−3.5x=33.6

42−x=33.6 or x=8.4cm

Point P should at 8.4 cm from vertex A.

Answer 2

Answer:

The area of the given  rectangle is 24 sq. cm.

Step-by-step explanation:

Given ABCD is a rectangle.

And APB is a triangle, inscribed in a rectangle.

Area of triangle APB,  $A = 12 sq. cm.$

Area of a triangle is given by half of the product of the height, h and the base, b of the triangle. i.e.,

$A=\dfrac{1}{2} \mbox{base}\times \mbox{height}$

Substituting the value of the area given,

$12=\dfrac{1}{2} \mbox{base}\times \mbox{height}$

$\implies \mbox{base}\times \mbox{height}=12\times 2=24sq.cm$                        

Area of rectangle is given by the product of its length and the breadth. i.e., $A=\mbox{length}\times\mbox{breadth}$

Base of the triangle is nothing but the length of the rectangle and height of the triangle is the breadth of the rectangle.

so, base x height = length x breadth

Therefore, the area of the given  rectangle is 24 sq. cm.

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