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What is the area of a right angled triangle if its sides are 6cm, 8cm and 10cm?

Given that sin $A=\frac{1}{2}$ and $cosB=\frac{1}{\sqrt{2}}$, then the value of (A + B) is:

CDE is an equilateral triangle formed on a side a CD of a square ABCD. Show that $\Delta ADE\cong \Delta BCE.$

Question 3

In the given figure, $\angle PQR={100}^{\circ }$, where P, Q and R are points on a circle with centre O. Find $\angle OPR$.

The mean of 23 observations is 34. If the mean of the first 12 observations is 32, and that of last 12 observations is 38, find the 12th observation.

Suppose that we have two triangles ∆ ABC and∆PQR with their corresponding sides are AB and PQ, BC and QR, AC and PR. After we proved triangle ABC congruent to triangle PQR by SSS test then is it compulsory to write triangle ABC congruent to triangle PQR in a particular way that is their names must be in correspondence with each other.

ABCD is a parallelogram. Find $\angle$ ADC.

Find the area of the shaded part in the figure given below. [Take $\pi =\frac{22}{7}$ and all the dimensions are in $cm$]

The height of an equilateral triangle measures 9 cm. Find its area, correct to 2 places of decimal. $(Take\sqrt{3}=\mathrm{1.732.})$

In the given figure, ΔPQR is an equilateral triangle and ΔPSR is right angled isosceles triangle right angled at S. If the coordinates of the vertices P, Q, R and S are (–x, 0), (0, y), (x, 0) and (0, z) respectively, then the area (in sq. units) of quadrilateral PQRS is



दिये गये चित्र में, ΔPQR एक समबाहु त्रिभुज है तथा ΔPSR समकोण समद्विबाहु त्रिभुज है जो S पर समकोण है। यदि शीर्षों P, Q, R व S के निर्देशांक क्रमशः (–x, 0), (0, y), (x, 0) व (0, z) हैं, तब चतुर्भुज PQRS का क्षेत्रफल (वर्ग इकाई में) है

Will you be able to draw a triangle if its base, a base angle and the difference of the other two sides is given?

​Answer True if yes else enter False.

1. Yes

   
   

The parallelogram PQRS is formed by joining together four equilateral triangles of side 1 unit, as shown in the figure.

What is the length of the diagonal SQ?

In the following figure, ED = EC. Then, which of the following are true?

Find the values of $x$ and $y$ that satisfy both the given equations.

$y-2x=4$ and $y-3x=2$

Which of the following expressions are polynomials? In case of a polynomial, write its degree.

(i) $x^5-2x^3+x+\sqrt{3}$

(ii) $y^3+\sqrt{3}y$

(iii) $t^2-\frac{2}{5}t+\sqrt{5}$

Three coins are tossed simultaneously $200$ times with the following frequencies of different outcomes:

Outcome	$3$ heads	$2$ heads	$1$ head	No head
Frequency	$23$	$72$	$77$	$28$

If the three coins are simultaneously tossed again, compute the probability of $2$ heads coming up.

The figure formed by joining the midpoints of the adjacent sides of a rhombus is a

(a) rhombus

(b) square

(c) rectangle

(d) parallelogram

In the given equation 4x+ 3y - 6 = 0 find the value of y when x = -3

From Fig, choose the letter(s) that indicate the location of the points given below:







(i) (2, 1)



(ii) (0, 5)



(iii) (2, 0)



Also write



(iv) The coordinates of A.



(v) The coordinates of F. [4 MARKS]

In a ${45}^{\circ }-{45}^{\circ }-{90}^{\circ }$ triangle, the length of the hypotenuse is $9\sqrt{2}$. What is the length of its sides?

$Ina\Delta ABC,itisgiventhat\angle A:\angle B:\angle C=3:2:1andCD\perp AC.Find\angle ECD.$

Steps of construction:
Step 1: Draw a line segment BC=5 cm
Step 2: Find the mid –point O of BC
Step 3 will be

If 40 bags of cotton costs ₹ 2,200, then how much would 25 bags of cotton cost?

For which of the following can a perpendicular bisector be drawn?