Question

Mensuration

1. Write 'True' or 'False' for the following statements :
(a) Every rectangle is a square.
(b) Diagonals of a rhombus bisect at right angles.
(c) Every rectangle is a parallelogram.
(d) Both diagonals of a parallelogram are equal.
(e) Rhombus is a parallelogram with all sides equal.
2. Area of a circle with diameter 14 cm. is. _​

Answer 1

Answer:

a.true

b.true

c.false

d.true

e.true

2.153.94 cm square

Answer 2

Answer:

(a) All rectangles are squares

Answer: All squares are rectangles but all rectangles can’t be squares, so this statement is false.

(b) In a rhombus , the diagonal (lines linking opposite corners) bisect each other at right angles (90°), That is each diagonal cuts the other into two equal parts, and the angle where they cross is always 90 degree. so it is true

(c) Not all parallelograms are rectangles. A parallelogram is a rectangle if it has four right angles and two pairs of parallel and congruent sides. so it is false

(d) When a parallelogram is divided into two triangles we get to see that the angles across the common side( here the diagonal) are equal. This proves that the opposite angles in a parallelogram are also equal. ... The diagonals of a parallelogram are not of equal length. so it is false

(e) In plane Euclidean geometry, a rhombus (plural rhombi or rhombuses) is a quadrilateral whose four sides all have the same length. ... Every rhombus is simple (non-self-intersecting), and is a special case of a parallelogram and a kite. A rhombus with right angles is a square. so it is true

2. Using the formulas

A=πr2

d=2r

Solving forA

A=1

4πd2=1

4·π·142≈153.93804cm²