Embibe Experts Solutions for Chapter: Areas of Parallelograms and Triangles, Exercise 1: Exercise

While preparing an Origami, Asmita folds a rectangular paper $PQRS$ is such a way that side $QR$ becomes $QT$. If the length of $PQ$ is $5 \mathrm{cm}$ and the length of $QR$ is $10 \mathrm{cm}$, what is the area of triangle $△PQU$?

Gia and Mia were discussing the different results that they found while finding the area of a parallelogram during their exams.

Gia: Parallelograms on the same base and between the same parallels are equal in area.

Mia: A rectangle and a parallelogram on the same base and between the same parallels are equal in area. 

Who is correct?

Two friends, Mohit and Rishav, learned about the area of parallelograms on the same base and between the same parallels in their Maths class today. While going through the same topic in their textbook, Mohit found two parallelograms on a unit square grid as shown below:

Mohit wanted to compare area of both the parallelograms. He asked Rishav for help. Rishav compared the area and replied that

A door which is in the form of a square has an area of $144 {\mathrm{cm}}^2$. The shadow of the door is in the form of a parallelogram which is represented by the figure respectively. Find the area of the shadow.

A flood relief camp was organised by state government for the people affected by the natural calamity near a city. Many school students volunteered to participate in the relief work. In the camp, food items and first aid centre kits were arranged for the flood victims. The piece of land used for this purpose is shown in the figure:

If $ABCD$ is a parallelogram with $E$ and $F$ as mid-points of sides $AB$ and $CD$ respectively, then show that are used for first aid is half of the total area.

Vishal wants to make some origami with coloured paper for his art and craft project in school. For this, he cut a triangle-shaped paper having two equal sides of $6 \mathrm{cm}$ each and one angle is a right angle. Then, he colours the middle portion of the triangle in a square as shown below:

Find the area of the square in ${\mathrm{cm}}^2$.