Mahabir Singh Solutions for Chapter: Heron's Formula, Exercise 3: ACHIEVERS SECTION (HOTS)

A design is made on a rectangular tile of dimensions $50 \mathrm{cm} x 70 \mathrm{cm}$ as shown in figure. The design shows $8$triangles, each of sides $26 \mathrm{cm}$, $17 \mathrm{cm}$ and $25 \mathrm{cm}$. Find the total area of the design and the remaining area of the tile respectively.

State ‘T’ for true and ‘F’ for false for each of the following statements:

(I) The lengths of the three sides of a triangular field are $40 \mathrm{m}, 24 \mathrm{m}$ and
$32 \mathrm{m}$ respectively. The area of the triangle $384 {\mathrm{m}}^2$.

(Il) The area of a quadrilateral $\mathrm{ABCD}$ in which $\mathrm{AB}=3 \mathrm{cm}, \mathrm{BC}=4 \mathrm{cm}, \mathrm{CD}=4 \mathrm{cm}$
$\mathrm{DA}=5 \mathrm{cm} \mathrm{and} \mathrm{AC}=5 \mathrm{cm} \mathrm{is}18 {\mathrm{cm}}^2$.

(Ill) An advertisement board is in the form of an isosceles triangle with its sides equal to $12 \mathrm{m}, 10 \mathrm{m} \mathrm{and} 10 \mathrm{m}.$ The cost of painting it at $₹2.25 \mathrm{per} {\mathrm{m}}^2$is $₹ 112.$

(IV) Heron’s formula cannot be used to calculate area of quadrilaterals.

Find the area of quadrilateral $\mathrm{ABCD}$ in which $\mathrm{AB}=9 \mathrm{cm} ,\mathrm{BC}= 40 \mathrm{cm}, \mathrm{CD}=28 \mathrm{cm}, \mathrm{DA}=15 \mathrm{cm} \mathrm{and} \mathrm{\angle }\mathrm{ABC}=90°$.